Question

use completing the square to solve for (x) in the equation ((x+7)(x-9) = 25).

\\(x = -4\\) or (6)
\\(x = -2\\) or (14)
\\(x = 1 \pm \sqrt{89}\\)
\\(x = 1 \pm \sqrt{87}\\)

Explanation:

Step 1: Expand the left side of the equation

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

Step 2: Move the constant term to the right side

$$x^2 - 2x = 88$$

Step 3: Complete the square by adding 1 to both sides

$$x^2 - 2x + 1 = 89$$

Step 4: Write the left side as a perfect square

$$(x - 1)^2 = 89$$

Step 5: Take the square root of both sides

$$x - 1 = \pm\sqrt{89}$$

Step 6: Solve for x

$$x = 1 \pm \sqrt{89}$$

Answer:

\(x = 1 \pm \sqrt{89}\)