Question

Solve 4x^2 + 16x - 84 = 0 by completing the square.

A) x = -4, x = 21
B) x = -3, x = 7
C) x = -7, x = 3
D) x = -21, x = 4

Answer 1

By completing the square, the equation 4x^2 + 16x - 84 = 0 is simplified to (x + 2)^2 = 25. After taking the square root of both sides, we find the solutions are x = -7 and x = 3, which matches answer option C.

Step-by-step explanation:

To solve the equation 4x^2 + 16x - 84 = 0 by completing the square, we need to manipulate it into the form (x+p)^2 = q, where p and q are some constants. First, we divide the entire equation by 4 to simplify our coefficients:

• x^2 + 4x - 21 = 0

We then complete the square by taking (4/2)^2 = 4 and adding it to both sides after moving the constant term to the opposite side:

• x^2 + 4x + 4 = 21 + 4
• (x + 2)^2 = 25

Now, we take the square root of both sides:

• x + 2 = ±5

Finally, we solve for x to find the two solutions:

• x = -2 - 5 or x = -2 + 5
• x = -7 or x = 3

Therefore, the correct answer is C) x = -7, x = 3.