Solve the quadratic equations

2 (x-2) ^2+5=23

2 (x^2-4x+4) = 18

2x^2-8x-10=0

(2x-10) (x+1)

X=5,-1

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).