PEAZIT Aha card
Go straight to resources ↓Square equations: remember both signs
Squaring loses the sign: both 4² and (−4)² equal 16. Solving x² = 16 therefore needs both possibilities.
| x value | Square |
|---|---|
| −4 | 16 |
| 4 | 16 |
One worked example
- x² + 9 = 25Isolate the squared expression first.
- x² = 16Subtract 9 from both sides.
- x = −4 or x = 4Check both values: each has square 16.
Watch out: √25 denotes only the nonnegative root 5, but x² = 25 has two solutions. x² = 0 has one; x² = −1 has no real solution. This method does not solve every quadratic equation directly.
Goal, prerequisites and card origin
What you will learn: Solve equations of the form x² = a over the real numbers.
What you need first: Squares, square roots and equation transformations.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
Squaring loses the sign: both 4² and (−4)² equal 16. Solving x² = 16 therefore needs both possibilities.