Solve the equation by completing the square. Round to the nearest hundreth if necessary. X^2 + 8x = 153(1 point)

Question

Responses

X= -9, 17

X= 17, -17

X=9, -17

X= 13, -13

Answer 1

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