Question

Solve by completing the square: j² + 6j - 7 = 0

Answer 1

To solve the quadratic equation j² + 6j - 7 = 0 by completing the square, follow these steps: Move the constant term to the right side of the equation, complete the square by adding the square of half the coefficient of the j term to both sides of the equation, take the square root of both sides to solve for j + 3, solve for j by subtracting 3 from both sides. Therefore, the solutions to the equation are j = -7 and j = 1.

Step-by-step explanation:

To solve the quadratic equation j² + 6j - 7 = 0 by completing the square, follow these steps:

1. Move the constant term to the right side of the equation: j² + 6j = 7
2. Complete the square by adding the square of half the coefficient of the j term to both sides of the equation:
   j² + 6j + (6/2)² = 7 + (6/2)²
   j² + 6j + 9 = 7 + 9
   (j + 3)² = 16
3. Take the square root of both sides to solve for j + 3:
   j + 3 = ±√16
   j + 3 = ±4
4. Solve for j by subtracting 3 from both sides:
   j = -3 ± 4

Therefore, the solutions to the equation are j = -7 and j = 1.