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= 17, -17
X=9, -17
X= 13, -13
To solve the equation by completing the square, we need to add and subtract the square of half the coefficient of x to both sides of the equation.
Given equation: x^2 + 8x = 153
Add and subtract (8/2)^2 = 16 to complete the square:
x^2 + 8x + 16 = 153 + 16
(x + 4)^2 = 169
Now take the square root of both sides:
x + 4 = ±√169
x + 4 = ±13
Now solve for x:
x = -4 ± 13
x = -4 + 13 = 9
x = -4 - 13 = -17
Therefore, the solutions are x = 9 and x = -17. Rounded to the nearest hundredth, the solutions are x = 9 and x = -17. So the correct answer is:
X = 9, -17