Solve the equation by completing the square.
x squared plus 9 x minus 14 equals 0
To solve this equation by completing the square, follow these steps:
1. Rewrite the equation in the form x^2 + bx = -c:
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. Rewrite the left side as a squared binomial:
(x + 9/2)^2 = 14 + 81/4
4. Solve for x by taking the square root of both sides:
x + 9/2 = ±√(14 + 81/4)
x + 9/2 = ±√(56/4 + 81/4)
x + 9/2 = ±√(137/4)
x + 9/2 = ±√137 / 2
5. Solve for x:
x = -9/2 ± √137 / 2
Therefore, the solutions to the equation x^2 + 9x - 14 = 0 are x = (-9 + √137) / 2 and x = (-9 - √137) / 2.