Question

Completing the square
x^2 -2x -43=5

Answer 1

x² - 2x - 43 = 5
- 5 - 5
x² - 2x - 48 = 0
x = -(-2) +/- √((-2)² - 4(1)(-48))
2(1)
x = 2 +/- √(4 + 192)
2
x = 2 +/- √(196)
2
x = 2 +/- 14
2
x = 1 +/- 7
x = 1 + 7 ∨ x = 1 - 7
x = 8 ∨ x = -6

Answer 2

`x^2-2x-43=5 \\ x^2-2x+1-1-43=5 \\ (x-1)^2-44=5 \\ (x-1)^2=49 \\ √((x-1)^2)=√(49) \\ |x-1|=7 \\ x-1=7 \ \lor \ x-1=-7 \\ x=8 \ \lor \ x=-6 \\ \boxed{x=-6 \hbox{ or } x=8}`