Question

Solve the quadratic equation by completing the square.

4x2 + 8x - 7 = 0

Answer 1

To solve the quadratic equation by completing the square, follow the steps properly mentioned in the detailed answer.

Step-by-step explanation:

To solve the quadratic equation: 4x2 + 8x - 7 = 0 by completing the square, follow these steps:

1. Move the constant term to the other side of the equation, so it becomes 4x2 + 8x = 7.
2. Divide the entire equation by the coefficient of x2, which is 4. This gives us x2 + 2x = 7/4.
3. Take half of the coefficient of x (which is 2) and square it. Add this value to both sides of the equation. x2 + 2x + 1 = 7/4 + 1.
4. Simplify the equation: x2 + 2x + 1 = 11/4.
5. Factor the left side of the equation: (x + 1)(x + 1) = 11/4.
6. Solve for x by taking the square root of both sides: x + 1 = ±√(11/4).
7. Isolate x by subtracting 1 from both sides: x = ±√(11/4) - 1.
8. Complete the square root calculations to get the final solutions for x.

Therefore, the solutions to the quadratic equation 4x2 + 8x - 7 = 0 are x = -1 + √(11/4) and x = -1 - √(11/4).