Question

question
which equation has the same solution as ( x^2 - 2x - 13 = -5 )?
answer
( (x + 1)^2 = 9 )
( (x + 1)^2 = 7 )
( (x - 1)^2 = 7 )
( (x - 1)^2 = 9 )

Explanation:

Step1: Simplify the original equation

$x^2 - 2x - 13 = -5$
$x^2 - 2x - 8 = 0$

Step2: Complete the square for $x^2-2x$

$x^2 - 2x = (x-1)^2 - 1$
Substitute into the equation:
$(x-1)^2 - 1 - 8 = 0$

Step3: Simplify to match the options

$(x-1)^2 - 9 = 0$
$(x-1)^2 = 9$

Answer:

$\boldsymbol{(x-1)^2 = 9}$