Question

Find the roots of the quadratic equation x2 – 8x = 9 by completing the square. Show your work.

Answer 1

Answer:

The answer is -1 or 9

The quadratic equation is ax² + bx + c  = 0. But, by completing the square we turn it into: a(x + d)² + e = 0, where:

d = b/2a

e = c - b²/4a

Our quadratic equation is x² - 8x = 9, which is after rearrangement:

x² - 8x - 9 = 0

So, a = 1, b = -8, c = -9

Let's first calculate d and e:

d = b/2a = -8/(2 * 1) = -8/2 = -4

e = c - b²/4a = -9 - (-8)²/(4 * 1) = -9 - 64/4 = -9 - 16 = -25

By completing the square we have:

a(x + d)² + e = 0

1(x + (-4))² + (-25) = 0

(x - 4)² - 25 = 0

(x - 4)² = 25

⇒ x - 4 = √25

Since √25 can be either -5  or +5 , then:

x - 4 = -5             or           x - 4 = 5

x = -5 + 4            or           x = 5 + 4

x = -1                   or           x = 9

Step-by-step explanation: