Question

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

Answer 1

Answer:

x = 1 + sqrt(89) or x = 1 - sqrt(89)

Step-by-step explanation:

Solve for x:

(x - 9) (x + 7) = 25

Expand out terms of the left hand side:

x^2 - 2 x - 63 = 25

Add 63 to both sides:

x^2 - 2 x = 88

Add 1 to both sides:

x^2 - 2 x + 1 = 89

Write the left hand side as a square:

(x - 1)^2 = 89

Take the square root of both sides:

x - 1 = sqrt(89) or x - 1 = -sqrt(89)

Add 1 to both sides:

x = 1 + sqrt(89) or x - 1 = -sqrt(89)

Add 1 to both sides:

Answer: x = 1 + sqrt(89) or x = 1 - sqrt(89)