Question

use completing the square to solve for x in the equation (x+7)(x-9)=25.\
\\(\bigcirc\\) \\(x = -4\\) or \\(6\\)\
\\(\bigcirc\\) \\(x = -2\\) or \\(14\\)\
\\(\bigcirc\\) \\(x = 1\pm \sqrt{89}\\)\
\\(\bigcirc\\) \\(x = 1\pm \sqrt{87}\\)

Explanation:

Step1: Expand left-hand side

$(x+7)(x-9) = x^2 - 9x + 7x - 63 = x^2 - 2x - 63$
Set equal to 25:
$x^2 - 2x - 63 = 25$

Step2: Isolate constant terms

$x^2 - 2x = 25 + 63$
$x^2 - 2x = 88$

Step3: Complete the square

Add $(\frac{-2}{2})^2 = 1$ to both sides:
$x^2 - 2x + 1 = 88 + 1$
$(x-1)^2 = 89$

Step4: Solve for x

Take square roots of both sides:
$x - 1 = \pm\sqrt{89}$
$x = 1 \pm\sqrt{89}$

Answer:

$x=1\pm\sqrt{89}$ (Option C)