Use completing the square to solve for in the equation (x - 12) (x + 4) = 9.

A quadratic equation is in the form of ax² + bx + c = 0. To find the roots of the quadratic equation we can use completing the square method.

Answer: By using completing the square method, equation (x - 12) (x + 4) = 9 can be solved as x = (4 + √ 73) or (4 - √ 73)

Let us proceed step by step.

Explanation:

Step 1: Rearrange the equation in the form of ax² + bx = c, if necessary.

⇒(x - 12) (x + 4) = 9

⇒x² - 8x - 57 = 0

Step 2: Add (b/2)² on both the sides of the equation, b = - 8 (coefficient of x)

⇒ x² - 8x + (- 8/2)² = 57 + (- 8/2)²

⇒ x² - 2 (x) (4) + (-4)² = 57 + (- 4)²

Step 3: Factorize the sides using algebraic identity (a - b)² into perfect squares.

⇒ (x - 4)² = 57 + 16

Step 4: Square root on both the sides.

⇒ √(x - 4)² = ±√73

Step 5: Solve for x

⇒ x - 4 = ± √73

⇒ x =  ±√ 73 + 4

⇒ x = 4 + √ 73 or 4 - √ 73

We can solve the quadratic equation using Cuemath's online quadratic equation calculator.

Therefore, by using completing the square method, equation (x - 12) (x + 4) = 9 can be solved as x = 4 + √ 73 or 4 - √ 73.