Solve the equation by completing the square. x2+9x-14=0(1 point)
To complete the square for the equation x^2 + 9x - 14 = 0, 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 (which is 9) and square it:
(9/2)^2 = (9/2)(9/2) = 81/4
3. Add the result from step 2 to both sides of the equation:
x^2 + 9x + 81/4 = 14 + 81/4
x^2 + 9x + 81/4 = 56/4 + 81/4
x^2 + 9x + 81/4 = 137/4
4. Now, rewrite the left side of the equation as a squared binomial:
(x + 9/2)^2 = 137/4
5. Take the square root of both sides to solve for x:
x + 9/2 = ±√(137)/2
6. Subtract 9/2 from both sides to solve for x:
x = -9/2 ± √(137)/2
Therefore, the solutions to the equation x^2 + 9x - 14 = 0 are:
x = -9/2 + √(137)/2
x = -9/2 - √(137)/2
Solve the equation by completing the square. x2+9x-14=0(1 point)
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 (which is 9) and square it:
(9/2)^2 = 81/4
3. Add the result from step 2 to both sides of the equation:
x^2 + 9x + 81/4 = 14 + 81/4
(x + 9/2)^2 = 56/4 + 81/4
(x + 9/2)^2 = 137/4
4. Take the square root of both sides to solve for x:
x + 9/2 = ±√(137)/2
5. Subtract 9/2 from both sides to solve for x:
x = -9/2 ± √(137)/2
Therefore, the solutions to the equation x^2 + 9x - 14 = 0 are:
x = -9/2 + √137/2
x = -9/2 - √137/2
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
It seems like you are providing a list of possible solutions for the equation x^2 + 9x - 14 = 0. Among the solutions you have listed, the correct solutions are:
x = 10.35
x = -1.35
These are the correct solutions to the quadratic equation x^2 + 9x - 14 = 0. Thank you for providing the solutions.