Question

Select the correct answer.Solve the equation using the method of completing the square.A. B. C. D.

Answer 1

C. -4 ± 2√6

Step-by-step explanation:

The given equation is

3x² + 24x - 24 = 0

First, add 24 to both sides

3x² + 24x - 24 + 24 = 0 + 24

3x² + 24x = 24

And factorize 3 on the left side

3(x² + 8x) = 24

Then, to complete the square, we need to add and substract (b/2)² to the expression in parenthesis. In this case, b = 8, so

(b/2)² = (8/2)² = 4² = 16

Then, add and subtract 16 as follows

3(x² + 8x + 16 - 16) = 24

3(x² + 8x + 16) - 3(16) = 24

3(x² + 8x + 16) - 48 = 24

Finally, we can factorize and solve for x

3(x + 4)² - 48 = 24

3(x + 4)² - 48 + 48 = 24 + 48

3(x + 4)² = 72

3(x + 4)²/3 = 72/3

(x + 4)² = 24

Solving for x, we get

`\begin{gathered} x+4=\pm√(24) \\ x+4-4=-4\pm√(24) \\ x=-4\pm√(24) \\ x=-4\pm√(4\cdot6) \\ x=-4\pm2√(6) \end{gathered}`

Therefore, the answer is

C. -4 ± 2√6