Solve the equation by completing the square.
x squared plus 9 x minus 14 equals 0
(1 point)
Responses
10.35, 1.35
10.35, 1.35
10.35, negative 1 point 35
10.35, Image with alt text: negative 1 point 35
negative 10.35, negative 1.35
Image with alt text: negative 10.35, negative 1.35
negative 10.35, 1.35
The equation is x^2 + 9x - 14 = 0.
Step 1: Move the constant term to the other side:
x^2 + 9x = 14
Step 2: To complete the square, take half of the coefficient of x (9/2 = 4.5) and square it (4.5^2 = 20.25), then add and subtract it inside the parentheses:
x^2 + 9x + 20.25 = 14 + 20.25
(x + 4.5)^2 = 34.25
Step 3: Take the square root of both sides to solve for x:
x + 4.5 = ±√34.25
x + 4.5 = ±5.85
Step 4: Solve for x:
x = -4.5 ± 5.85
x = 1.35 or x = -10.35
Therefore, the solutions are x = 1.35 and x = -10.35.