2(x-2)² + 5 = 23
2(x² - 4x + 4) + 5 = 23
2x² - 8x + 8 + 5 = 23
2x² - 8x + 13 = 23
2x² - 8x + 13 - 23 = 0
2x² - 8x - 10 = 0
2(x² - 4x - 5) = 0
Divide both sides by 2
x² - 4x - 5 = 0
Factor:
(x - 5)(x + 1) = 0
Set both factors equal to zero:
x - 5 = 0
x = 5
x + 1 = 0
x = - 1
Your answers are x = -1, 5 or at (-1, 0) and (5, 0).
