Question

Solve the equation 5 = (2/5)(x + 3)² using the square root method.

A. x = -13
B. x = -5
C. x = 1
D. x = 13

Answer 1

After solving the equation 5 = (2/5)(x + 3)² using the square root method, the solutions are approximately x = 0.54 and x = -6.54, which do not exactly match any of the provided options.

Step-by-step explanation:

To solve the equation 5 = (2/5)(x + 3)² using the square root method, follow these steps:

1. Multiply both sides of the equation by the reciprocal of (2/5) to isolate the squared term:
2. 5 * (5/2) = (x + 3)²
3. Now calculate the left side:
4. 25/2 = (x + 3)²
5. Take the square root of both sides:
6. ±√(25/2) = x + 3
7. Solve for x:
8. x = -3 ± √(25/2)
9. There are two possible solutions after calculating the square roots:
10. x = -3 + √(25/2) or x = -3 - √(25/2)
11. However, we must check which of the provided options match our solutions. Option A: x = -13 and Option B: x = -5 could be possible but we need to calculate the exact values.

Calculating the square root of 25/2 gives us approximately 3.54. Therefore, our solutions are:

x = -3 + 3.54 or x = -3 - 3.54

x = 0.54 or x = -6.54

Looking at our options, Option B: x = -5 is closest to one of our solutions. However, since none of the options exactly match, we need to clarify that the actual solutions are approximately 0.54 and -6.54 which are not listed among the options.