SHIFT SOLVE is the key sequence that turns a scientific calculator into a numerical equation solver. You type an equation, press SHIFT then SOLVE, give it a starting guess, and it finds a value that makes both sides equal. This guide walks through WideMath's own SHIFT SOLVE: a real equation from start to finish, why your guess changes which root you get, what the L − R number means, and the errors you will run into along the way.
On this page
What SHIFT SOLVE does
SHIFT SOLVE finds a value for one unknown letter that makes an equation true, by trying a number, checking how close it is, and adjusting, over and over, until the result stops moving. You give it a starting guess. It does the algebra you would otherwise do by hand, or in some cases could not do by hand at all.
Underneath, WideMath's SHIFT SOLVE runs Newton's method: it checks how steep the equation is at your guess, steps to where that slope would hit zero, and repeats, up to 100 times. It is the same numerical idea behind the equation solver on Casio's handheld calculators: without a guess, there is nowhere to start stepping from.
How to type an equation SHIFT SOLVE can read
If SHIFT and ALPHA are new to you, our beginner's guide to a scientific calculator covers the keypad basics first. For SHIFT SOLVE, three things decide whether it understands what you typed.
SOLVE lives on the SHIFT layer of CALC. Press SHIFT, then CALC, once your equation is on screen.
The unknown is the letter X, typed with ALPHA. On WideMath's on-screen keypad, X sits on the ALPHA layer of the ")" key: press ALPHA, then ")". If you are typing on a physical keyboard instead of clicking, just press the X key. Letters go in as variables automatically, no ALPHA needed.
The equals sign is ALPHA CALC, not the key that finishes a sum. Press ALPHA, then CALC, to type "=". You do not have to use it at all: leave the equals sign off and WideMath reads whatever you typed as the left side of "= 0". X² − 5X + 6 and X² − 5X + 6 = 0 reach SHIFT SOLVE the same way.
X is the default, but it is not the only letter available. WideMath has nine variable letters in total: A to F, X, Y and M. To solve for one of the others, end the whole line with a comma and that letter, for example ending in ,Y solves for Y instead of X. The comma is the SHIFT layer of the same ")" key. Any other letter that shows up in the equation is treated as a known value, and SHIFT SOLVE asks you for it before it asks for a guess.
On Casio's fx-991 calculators, the equation solver only accepts X: asking it to solve for another letter throws a variable error, according to independent testing of the fx-991EX. WideMath's SHIFT SOLVE is not limited that way. It accepts any of its nine variable letters.
Step by step: solving X² − 5X + 6 = 0
Open WideMath and try this alongside the guide. X² − 5X + 6 = 0 has two whole-number roots, 2 and 3, which makes it easy to check whether SHIFT SOLVE actually got it right.
Type the equation. Press ALPHA then ")" for X, tap the dedicated x² key, then finish normally: X²−5X+6. No equals sign needed.
Press SHIFT then CALC. A panel opens, titled SOLVE, asking for "X (initial guess)". Nothing is stored in X yet, so it suggests 1.
Leave the guess at 1 and press Solve. The display shows X=2. The panel also shows L − R, at or almost exactly 0.
Check the root by hand: 2² − 5×2 + 6 = 0
X² − 5X + 6 = 0 is a quadratic, so it has a second root, and SHIFT SOLVE only ever hands back one answer per attempt: the one nearest wherever your guess started. Finding the other root means solving again with a different starting point.
Press SHIFT then CALC again on the same equation. The guess field now suggests 2, the root it just found. Clear that and type 5 instead.
Press Solve. The display now shows X=3, the second root.
Check the second root the same way: 3² − 5×3 + 6 = 0
Same equation, same key sequence, a different answer, because Newton's method does not scan the whole number line. It steps downhill from wherever you put it, so the root it lands on depends on where that walk begins. A guess of 0 or 1 falls toward the smaller root here; a guess of 4 or 5 falls toward the larger one.
L − R is the leftover when you put the answer back into the original equation, left side minus right side. For this equation that is (X² − 5X + 6) minus 0, recalculated at whatever X the calculator landed on. A genuine root drives that number to 0, or close enough that the gap is rounding noise rather than a real error. If L − R came back as something like 0.4, that would be a sign SHIFT SOLVE settled near an answer without truly finding one.
Solving a formula for any variable
SHIFT SOLVE is not only for equations that already have a bare X sitting in them. It will solve a real formula for whichever piece you do not know, without you rearranging anything first.
Take the volume of a cylinder, V = πr²h. Say a tank holds 40π cubic metres and stands 10 metres tall. What is its radius? By hand, that means dividing by π and by the height, then taking a square root: easy to fumble under exam pressure.
Type the formula with a real equals sign this time, radius as X, volume as A, height typed directly as the number 10: A=π×X²×10. Get "=" from ALPHA CALC, and A from ALPHA plus its own key.
Press SHIFT then CALC. The panel now asks for two things in order: "A =", because A appears in the equation and is not the letter being solved for, then "X (initial guess)".
For A, type 40×π so the calculator works with the exact value instead of a rounded one. For the guess, 1 is close enough to converge: type it if the field is not already showing it.
Press Solve. The display shows X=2: a 2 metre radius.
Confirm it: a cylinder 2 metres across and 10 metres tall holds exactly 40π: π×2²×10 = 40π
Every other letter in the equation gets its own prompt before the guess does, pre-filled with whatever that letter last held in memory, so SHIFT SOLVE remembers values you already stored. Whatever you type in gets saved back into that same memory too, so A keeps its value if you solve the equation again.
Common SHIFT SOLVE errors
If SHIFT SOLVE is not working the way you expect, it is almost always one of four things.
The panel says "Can't Solve, try a different initial value." This means 100 rounds of stepping never settled down, and the last value tried was not already close to zero either. The fix is usually exactly what the message says: pick a different starting guess, ideally nearer to where you expect the real answer to sit.
Some equations have no real answer to find at all. X² + 1 = 0 is the standard example: X² is never negative, so X² + 1 never drops below 1, and it can never reach 0. SHIFT SOLVE only searches real numbers, so no starting guess will ever fix this one.
See the floor for yourself: 0² + 1 = 1, the lowest X² + 1 ever gets.
This shows up if you press SHIFT SOLVE with nothing typed, or if the equation does not parse, most often a stray bracket left over from tapping ")" when you meant ALPHA then ")" for X.
On screen, X is not its own key: it is the ALPHA layer of ")". Tap ")" on its own and you get a parenthesis in the equation instead of a variable, which is the usual cause of the Syntax ERROR above. This does not apply on a physical keyboard, where typing X inserts the variable directly.
SHIFT SOLVE vs EQN mode vs solving by hand
WideMath has three ways to find an unknown, and they are not interchangeable.
| SHIFT SOLVE | EQN mode | By hand | |
|---|---|---|---|
| Best for | One equation, one unknown, any shape | Quadratics, cubics, 2 to 3 linear equations | Understanding why the answer is true |
| Roots per run | One, nearest your guess | All of them, at once | All of them, if the algebra is right |
| Needs rearranging first? | No | No, just the coefficients | Usually, yes |
| Handles logs, trig, mixed letters? | Yes | No, coefficients only | Yes, with the right method |
| Complex roots? | No, real numbers only | Yes | Yes, with the right method |
| Typical failure | Can't Solve, from a poor guess | None, if the equation fits the mode | A dropped sign or a missed case |
For a plain quadratic or cubic, or 2 to 3 linear equations solved together, EQN mode is faster: it takes the coefficients and returns every root at once, real or complex, with nothing to guess. Our equation solver guide covers it in full. Reach for SHIFT SOLVE when the equation will not fit EQN's coefficient boxes: logs, trig, square roots, or several letters mixed together the way the cylinder formula was.
One more thing to check before you solve: if your equation includes sin, cos or tan, confirm your angle mode first. SHIFT SOLVE reads them the same way the rest of WideMath does, so an equation solved in degrees will not match one solved in radians. Our guide to degrees and radians covers the difference.
Try SHIFT SOLVE yourself
Free, no sign-up, and the same SHIFT and ALPHA layout as the calculator in your bag.
Open the scientific calculator →Questions people ask
What does SHIFT SOLVE do on a scientific calculator?
SHIFT SOLVE is a numerical equation solver. You type an equation, press SHIFT then the SOLVE key, give it a starting guess for the unknown, and it uses Newton's method to walk from that guess to a value that makes the equation true.
How do I type the equals sign for a SOLVE equation?
Press ALPHA then CALC. The plain equals key only finishes an ordinary sum. Typing no equals sign at all also works: WideMath reads the expression as equal to zero.
Why does SHIFT SOLVE say Can't Solve?
Either there is no real solution near your guess, or the guess landed somewhere the calculator's method has no slope to follow, such as a flat point. Try a different starting value, ideally closer to where you expect the answer to be.
Can SHIFT SOLVE find more than one root?
Not in a single attempt. It returns one root, the one nearest the path from your starting guess. An equation like X² − 5X + 6 = 0 has two roots, 2 and 3, and you get each one by solving twice with a different guess.
Does my equation have to be set to zero?
No. Type X² − 5X + 6 = 0 using ALPHA CALC for the equals sign, or leave the equals sign off entirely: X² − 5X + 6 alone is read the same way.
When should I use EQN mode instead of SHIFT SOLVE?
Use EQN mode for a plain quadratic, cubic, or a system of 2 to 3 linear equations: it works from the coefficients and returns every root at once, real or complex, with nothing to guess. SHIFT SOLVE covers equations EQN mode cannot, such as logs, trig or mixed variables, but it returns only one root per attempt.
Sources
- Newton's method, Wikipedia: how the iteration steps from a guess toward a root, and why a poor starting point can fail to converge.
- Equation Solve for X, fx-991EX, George Garside: the equivalent ALPHA CALC keystroke and the X-only limit on Casio's own equation solver.