How to solve an equation
- Type the equation, such as 3(x − 2) = 2x + 5. Write powers with ^ (x^2), and multiplication can be left out: 2x and 3(x + 1) both work.
- For several equations at once, put each on its own line or separate them with commas. To expand or factor, type the expression without an equals sign, or start with expand or factor.
- Read the answer and the working underneath. With more than one letter, type the one you want in Solve for.
What you can type
| You want to | Type |
|---|---|
| Solve a linear equation | 5x − 3 = 2x + 9 |
| Solve a quadratic | x^2 + 2x − 8 = 0 |
| Solve with fractions | x/3 + x/4 = 14 or 2/(x − 1) = 4 |
| Solve a system | 2x + y = 7, x − y = 2 |
| Rearrange a formula | v = u + at with Solve for set to t |
| Expand brackets | expand (x + 3)^2 |
| Factor | factor 2x^2 + 7x + 3 |
Letters are single variables, so xy means x times y. The letter e on its own is Euler’s number (2.718…) and pi is π.
How the steps work
The calculator does what you would on paper. It expands brackets and combines like terms, moves every x term to one side and every number to the other, then divides. For a quadratic it first tries to factor, because that’s quicker when the answers are neat. When they aren’t, it uses the quadratic formula, x = (−b ± √(b² − 4ac)) / 2a, and keeps the square root exact. For higher powers it tests the fractions that could be roots, divides each one out and finishes what’s left with the quadratic formula. Only when no exact method applies does it switch to a numerical search.
Checking an answer
Put the answer back into the original equation: both sides should come out equal. For 3(x − 2) = 2x + 5 and x = 11, the left side is 3 × 9 = 27 and the right is 22 + 5 = 27. It’s the quickest way to catch a sign slip when you’re working by hand, and for equations with x in a fraction it also shows whether an answer would divide by zero.