Solve the equation by completing the square. Round to the nearest hundreth if necessary. X^2 + 8x = 153(1 point)
Responses
X= -9, 17
X= -9, 17
X= 17, -17
X= 17, -17
X=9, -17
X=9, -17
X= 13, -13
To solve the equation by completing the square, follow these steps:
1. Move the constant term to the right side of the equation:
x^2 + 8x - 153 = 0
2. Divide the coefficient of x by 2 and square it:
(8/2)^2 = 16
3. Add and subtract this value inside the parentheses on the left side of the equation:
x^2 + 8x + 16 - 16 - 153 = 0
x^2 + 8x + 16 = 169
4. Factor the left side of the equation and simplify the right side:
(x + 4)^2 = 169
5. Take the square root of both sides:
x + 4 = ±√169
x + 4 = ±13
6. Solve for x:
x = -4 ± 13
x = -4 + 13 = 9
x = -4 - 13 = -17
Therefore, the solutions to the equation x^2 + 8x = 153 by completing the square are x = 9, -17. So the correct response is:
X= 9, -17