Question

Rewrite the equation by completing the square.
4x² + 28x + 49=0

Answer 1

To rewrite the equation by completing the square, follow these steps: move the constant term, divide and square the coefficient of x², add the squared term, factor the left side, take the square root, solve for x, and divide by 2.

Step-by-step explanation:

To rewrite the equation by completing the square, we follow these steps:

1. Move the constant term to the right side of the equation: 4x² + 28x = -49.
2. Divide the coefficient of x² by 2 and square it: (28/2)² = 196.
3. Add the squared term to both sides of the equation: 4x² + 28x + 196 = -49 + 196.
4. Factor the left side of the equation: (2x + 14)² = 147.
5. Take the square root of both sides: 2x + 14 = ±√147.
6. Solve for x: 2x = -14 ± √147.
7. Divide by 2 to get the final solutions: x = -7 ± (1/2)√147.