Mathematics
BobbieArgabright
46

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

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(1) Answers
ItssHannahh

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

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