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
X= 13, -13
To solve the equation by completing the square:
1. Move the constant term to the right side of the equation:
x^2 + 8x = 153
x^2 + 8x - 153 = 0
2. To complete the square, take half of the coefficient of x (8/2 = 4) and square it (4^2 = 16). Add and subtract this value inside the parentheses:
x^2 + 8x + 16 - 16 - 153 = 0
(x + 4)^2 - 169 = 0
3. Re-write the equation in standard form:
(x + 4)^2 = 169
4. Take the square root of both sides:
x + 4 = ± 13
5. Solve for x:
x = -4 ± 13
x = -17, 9
Therefore, the solutions to the equation are x = -17 and x = 9. So the correct answer is:
X = -17,9