Leo+DadMade for Leo
Solving Quadratic Equations
Rung 2 of 4 · The method

Actually Solving One

Get on its own, square-root both sides, write the ±. Three moves, and you've solved a quadratic.


PractiseHit “new equation”, solve it, reveal the steps to check yourself — then give both solutions.
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For the quadratics at this level, every one is the same three moves: get the by itself, square-root both sides, and remember the ±. No fancy formula needed.

The Three Moves

One — get x² on its own. If it already reads x² = 36, you're set. If it's x² − 36 = 0, add 36 to both sides (just like a linear equation) to get x² = 36 first.

Two — square-root both sides. The square root undoes the square: x = ±√36.

Three — write both signs. √36 = 6, so x = 6 or x = −6. The ± is not optional — more on why next rung.

A Worked One

Solve x² − 49 = 0. Add 49: x² = 49. Square-root: x = ±√49. And √49 = 7, so x = 7 or x = −7. Done.

Say it plainly: do the same to both sides until stands alone, then square-root both sides and keep the ±. Whatever you do to one side, do to the other — same rule as every equation.

Keep the Numbers Friendly

At this stage the right-hand side is a perfect square — 4, 9, 16, 25, 36… — so the root is a whole number you can often spot. If you can't recall it, the times-tables get you there: "7 times 7 is 49, so √49 = 7." Squaring built it; square-rooting takes it apart.

Us, Thinking Out Loud

Could you teach me the three moves without looking?

Why is "get x² on its own" the very first move?