Solve the equation by completing the square. x^2+9x-14=0(1 point) Responses 10.35, 1.35 10.35, 1.35 10.35, 10.35, Image with alt text: negative 1 point 35 Image with alt text: negative 10.35, negative 1.35 , 1.35
To solve the equation x^2 + 9x - 14 = 0 by completing the square, follow these steps:
1. Move the constant term to the other side of the equation:
x^2 + 9x = 14
2. To complete the square, take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 + 9x + (9/2)^2 = 14 + (9/2)^2
x^2 + 9x + 81/4 = 14 + 81/4
3. Simplify the equation:
x^2 + 9x + 81/4 = 56/4 + 81/4
x^2 + 9x + 81/4 = 137/4
4. Rewrite the left side of the equation as a perfect square trinomial:
(x + 9/2)^2 = 137/4
5. Take the square root of both sides to solve for x:
x + 9/2 = ±√(137/4)
6. Solve for x by subtracting 9/2 from both sides:
x = -9/2 ± √(137/4)
Therefore, the solutions to the equation x^2 + 9x - 14 = 0 are:
x = -9/2 ± √(137/4)
x ≈ -10.35, 1.35