Solve the equation by completing the square.
x° +9x-14=0
(1 point)
10.35, 1.35
• 10.35, -1.35
0-10.35,-1.35
O-10.35, 1.35
To solve the equation by completing the square, we want to rewrite it in the form of (x - h)^2 = k.
Given equation: x^2 + 9x - 14 = 0
1. Move the constant term to the other side:
x^2 + 9x = 14
2. Divide the coefficient of x by 2 and square it:
(9/2)^2 = 81/4
3. Add and subtract the result from step 2 inside the parentheses:
x^2 + 9x + 81/4 - 81/4 = 14
4. Rewrite it as a perfect square trinomial:
(x + 9/2)^2 - 81/4 = 14
5. Add 81/4 to both sides:
(x + 9/2)^2 = 14 + 81/4
(x + 9/2)^2 = 56/4 + 81/4
(x + 9/2)^2 = 137/4
6. Take the square root of both sides:
x + 9/2 = ±√(137)/2
x = -9/2 ± √(137)/2
x ≈ -10.35, 1.35
Therefore, the solutions are approximately x = -10.35, 1.35. The correct answer choice is:
• 10.35, -1.35