Q:

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

Accepted Solution

A:
Answer:The answer is -1 or 9The 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/2ae = c - b²/4aOur quadratic equation is x² - 8x = 9, which is after rearrangement:x² - 8x - 9 = 0So, a = 1, b = -8, c = -9Let's first calculate d and e:d = b/2a = -8/(2 * 1) = -8/2 = -4e = c - b²/4a = -9 - (-8)²/(4 * 1) = -9 - 64/4 = -9 - 16 = -25By completing the square we have:a(x + d)² + e = 01(x + (-4))² + (-25) = 0(x - 4)² - 25 = 0(x - 4)² = 25⇒ x - 4 = √25Since √25 can be either -5  or +5 , then:x - 4 = -5             or           x - 4 = 5x = -5 + 4            or           x = 5 + 4x = -1                   or           x = 9Step-by-step explanation: