x

y

solution

solution

If a quadratic equation is in the form ax2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots.

Solve By Square Roots

If , then and or ExampleIf x2 = 25, then x = ±5.

x c2x cx c x c

Solving Quadratics

Square Root Method:

02 cbxax

No bx term 21. 9x

2 9x

x 3, 3x 9, 9

or

3x

Solving Quadratics

Square Root Method:

02 cbxax

No bx term 22. 49 0 x

4949492x

2 49x x 7, 7 7xor

Solving Quadratics

Square Root Method:

02 cbxax

No bx term 23. 56x

2 56x

x 2 14, 2 14x 56, 56

2 14

Solve by taking square roots.3x2 - 24 = 0

Isolate x2

1.Add 24 to both sides.3x2 = 24

2.Divide both sides by 3.x2 = 8

3. Take the square root of both sides.

x 8 x 4 2

x 4 2

x 2 2

23 100 332x 23 432x

2 432144

3x

2 144x 12x

2( 3) 25x 2( 3) 25x 3 5x

3 5x 3 5x 3 3 5 3x 3 3 5 3x

2x 8x

23( 2) 4 52x 23( 2) 48x 2( 2) 16x

2( 2) 16x 2 4x

2 4x 2 4x 6x 2x