Answer :
[tex]x^2-2x-43=5 \\
x^2-2x+1-1-43=5 \\
(x-1)^2-44=5 \\
(x-1)^2=49 \\
\sqrt{(x-1)^2}=\sqrt{49} \\
|x-1|=7 \\
x-1=7 \ \lor \ x-1=-7 \\
x=8 \ \lor \ x=-6 \\
\boxed{x=-6 \hbox{ or } x=8}[/tex]
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
- 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