Question

The first few steps in solving the quadratic equation 8x² + 80x = −5 by completing the square are shown

8x² + 80x = −5

8(x² + 10x) = −5

8(x² + 10x + 25) = −5 + ______

Which number is missing in the last step?

a. -200
b. -25
c. 25
d. 200

Answer 1

To solve the quadratic equation 8x² + 80x = −5 by completing the square, follow the steps: Move the constant term to the right side, divide by the coefficient of x², complete the square, simplify, take the square root, and solve for x. The missing number in the last step is -25.

option b is the correct

Step-by-step explanation:

To solve the quadratic equation 8x² + 80x = −5 by completing the square, we follow these steps:

1. Move the constant term to the right side of the equation: 8x² + 80x + 5 = 0
2. Divide the entire equation by the coefficient of x² to make the coefficient 1: x² + 10x + 5/8 = 0
3. Complete the square by adding the square of half the coefficient of x to both sides of the equation: x² + 10x + 25 + 5/8 = 25
4. Simplify: (x + 5/2)² = 24 3/8
5. Take the square root of both sides: x + 5/2 = ±√(24 3/8)
6. Subtract 5/2 from both sides: x = -5/2 ±√(24 3/8) - 5/2

In the last step, the missing number is -25, so the answer is (c) -25.