Solve quadratic equations by taking square roots

Warm-up

Three quick questions from earlier lessons.

Discover

A square rug has an area of 49 square feet. Which numbers $x$ make $x^2 = 49$ true?

$7$ and $-7$
Only $7$

Key idea

Undo a square with ±.

x^2 = k

with

k > 0

, then

x = \sqrt{k}

x = -\sqrt{k}

. If

(x - h)^2 = k

, then

x - h = \pm\sqrt{k}

, so

x = h \pm \sqrt{k}

. Get the square alone first.

Worked example

Solve $(x - 3)^2 = 25$ .

x - 3 = 5

x - 3 = -5

Square roots.

x = 8

x = -2

Add 3.

Your turn, guided

Your turn: the positive solution of $2x^2 = 72$ .

6

x² = 36.

Practice ★

Solve $x^2 = 100$ . Enter all solutions.
Solve $x^2 = 25$ . Enter all solutions.

Solve $3x^2 - 3 = 0$ . Enter all solutions.

Watch out!

Practice ★★

Solve $(x - 7)^2 = 64$ . Enter all solutions.
Solve $(x - 8)^2 = 1$ . Enter all solutions.

Exit ticket

Three questions to check you have got it.

Solve $x^2 = 100$ . Enter all solutions.
Solve $x^2 = 25$ . Enter all solutions.
Solve $x^2 = 36$ . Enter all solutions.

Summary card

Solving by square roots

Isolate the square; then $\pm\sqrt{\;}$ .

Watch out: two solutions, not one.

End of the lesson

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