Question

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

Answer 1

Answer:

c

Step-by-step explanation:

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

x = –4 or 6

x = –2 or 14

x = 1 plus-or-minus StartRoot 89 EndRoot

x = 1 plus-or-minus StartRoot 87 EndRoot

Answer 2

Answer:

x = 1 ±√89

The correct option is C.

Step-by-step explanation:

To solve the equation; (x + 7(x-9) = 25, we will follow the steps below;

First, we will open the bracket

x² - 9x +  7x  - 63 = 25

x² - 2x  - 63 = 25

Add 63 to both-side of the equation

x² - 2x -63 + 63 = 25 + 63

x² - 2x = 88

We can now proceed to solve using the completing the square method.

Add the square of (-1) to both-side of the equation

x² - 2x + (-1)²= 88 + (-1)²

Factorize the left-hand side of the equation and simplify the right-hand side of the equation

(x - 1)² = 88 + 1

(x - 1)² = 89

Take the square root of both-side of the equation

√(x - 1)² = ±√89

x - 1 =±√89

Add 1 to both-side of the equation

x - 1+1 = 1 ±√89

x = 1 ±√89