Question

Solve the following quadratic equation by the square root property of equality.

2(x + 7)² = 64
A) x = -7
B) x = -5
C) x = 5
D) x = 7

Answer 1

After isolating the squared term and taking the square root of both sides, the solutions to the equation 2(x + 7)² = 64 are x = -7 ± 4√2, which simplifies to x = -1.344 and x = -12.656. However, these solutions do not match the multiple-choice options, indicating a possible error in the given question or options.

Step-by-step explanation:

To solve the given quadratic equation 2(x + 7)² = 64 by using the square root property of equality, we first isolate the squared term:

1. Divide both sides of the equation by 2 to get (x + 7)² = 32.
2. Take the square root of both sides to get x + 7 = ±√32. Since the square root of 32 is ± 4√2, our equation simplifies to x + 7 = ± 4√2.
3. Subtract 7 from both sides to isolate x and get x = -7 ± 4√2.

Since we know that √2 is approximately 1.414, multiplying it by 4 gives us approximately 5.656. Therefore, we have two solutions:

• x = -7 + 5.656, which simplifies to x = -1.344 (not an option in the multiple-choice answers)
• x = -7 - 5.656, which simplifies to x = -12.656 (also not an option)

There seems to be an error because neither of the answers matches the multiple-choice options provided. The student should verify the original equation or the list of options.