Question

What is the intermediate step in the form (x + a)² = b as a result of completing the square for the following equation? -3x² - 24x - 13 = -13

A) x² + 24x + a² = b
B) x² + 24x + 12 = b
C) (x + 12)² = b
D) x² + 24x + 144 = b

Answer 1

The intermediate step in completing the square for the equation -3x² - 24x - 13 = -13 is to add the squared value of half the coefficient of the x term to both sides of the equation.

Step-by-step explanation:

The intermediate step in completing the square for the equation -3x² - 24x - 13 = -13 is as follows:

Step 1: Move the constant term to the right side of the equation:

-3x² - 24x = 0

Step 2: Divide the coefficient of the x² term by 2 and square it:

(-24/2)² = 144

Step 3: Add the value obtained in step 2 to both sides of the equation:

-3x² - 24x + 144 = 0

Therefore, the correct answer is option D) x² + 24x + 144 = b.