solve the equation by completing the square
x^2 + 9x -14 = 0
A 10.35, 1.35
B 10.35, -1.35
C -10.35, -1.35
D -10.35, 1.35
To solve the equation by completing the square, first move the constant term over to the other side:
x^2 + 9x = 14
Next, take half of the coefficient of x (which is 9), square it, and add that value to both sides of the equation:
x^2 + 9x + (9/2)^2 = 14 + (9/2)^2
x^2 + 9x + 20.25 = 14 + 20.25
x^2 + 9x + 20.25 = 34.25
Now, rewrite the left side as a squared binomial:
(x + 4.5)^2 = 34.25
Take the square root of both sides to solve for x:
x + 4.5 = ±√34.25
x = -4.5 ± √34.25
x ≈ -4.5 ± 5.84
So, the solutions to the equation x^2 + 9x - 14 = 0 are:
x ≈ -4.5 + 5.84 = 1.34
x ≈ -4.5 - 5.84 = -10.34
Therefore, the correct answer is A) 10.35, 1.35