Question

Solve the equation using completing the square: p^2 + 4p = 12.

A) p = 2
B) p = -2
C) p = 3
D) p = -3

Answer 1

To solve the equation p^2 + 4p = 12 by completing the square, we transform it to (p + 2)^2 = 16 and then take the square root of both sides, resulting in p = 2 or p = -6. Only p = 2 matches the provided options.

Step-by-step explanation:

To solve the equation p^2 + 4p = 12 using completing the square, we need to manipulate the equation into a perfect square. Here's the step-by-step process:

• First, move the constant term to the right side of the equation: p^2 + 4p - 12 = 0.
• Then, divide all terms by the coefficient of the p^2 term, which is 1, so the equation remains unchanged.
• We want to form a perfect square trinomial on the left side, which requires adding the square of half the coefficient of p to both sides of the equation. In this case, half of 4 is 2, and the square of 2 is 4. So, we add 4 to both sides, obtaining p^2 + 4p + 4 = 16.
• The left side of the equation is now a perfect square: (p + 2)^2 = 16.
• Finally, take the square root of both sides and solve for p: p + 2 = ±4, which means p = -2 + 4 or p = -2 - 4.

These give us p = 2 and p = -6. However, only p = 2 matches one of the given options, which is answer A).