Use completing the square to solve for x in the equation (x - 12)(x + 4) = 9.A. x = -1 or 15B. x = 1 or 7C. x (plus sign over minus sign) square root of 41.D. x (plus sign over minus sign) square root of 73.Please help! This is timed!
Accepted Solution
A:
Solve for x over the real numbers by completing the square: (x - 12) (x + 4) = 9
Expand out terms of the left-hand side: x^2 - 8 x - 48 = 9
Add 48 to both sides: x^2 - 8 x = 57
Add 16 to both sides: x^2 - 8 x + 16 = 73
Write the left hand side as a square: (x - 4)^2 = 73
Take the square root of both sides: x - 4 = sqrt(73) or x - 4 = -sqrt(73)
Add 4 to both sides: x = 4 + sqrt(73) or x - 4 = -sqrt(73)
Add 4 to both sides:
Answer: x = 4 + sqrt(73) or x = 4 - sqrt(73) Thus the Answer is D: