Question

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

A)x= -4 or 6
B)x=-2 or 14
C)X=11 or 89
D)X=17 or87

Answer 1

To solve the equation (x+7)(x-9) = 25 using completing the square, we expand, rearrange, complete the square, and simplify to find x = 10 or x = -8.

Step-by-step explanation:

The question asks to solve for x in the equation (x+7)(x-9) = 25 using completing the square.

We start by expanding the left side to obtain x² - 2x - 63 = 25. Subtracting 25 from both sides gives us x² - 2x - 88 = 0. Now, to complete the square, we add the square of half the coefficient of x to both sides: x² - 2x + 1 = 88 + 1, leading to (x - 1)² = 89. The next step is to take the square root of both sides, which gives us x - 1 = ±√89. Adding 1 to both sides produces x = 1 ± √89, which simplifies to x = 1 + √89 or x = 1 - √89. Simplifying the square roots gives us the final answer x = 10 or x = -8.