Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 + 2x = 8

Question

x=2,4
x=-2,4
x=2, -4
x= -2 , -4

Answer 1

To complete the square for the equation x^2 + 2x = 8, we first need to move the constant term to the other side:

x^2 + 2x - 8 = 0

Now, we complete the square by taking half of the coefficient of x and squaring it.

2 divided by 2 is 1, and 1 squared is 1. Now we add and subtract 1 within the brackets:

x^2 + 2x + 1 - 1 - 8 = 0
(x + 1)^2 - 9 = 0

Now rewrite the equation in this form:

(x + 1)^2 - 9 = 0

Solve for x by adding 9 to both sides:

(x + 1)^2 = 9

Take the square root of both sides:

x + 1 = ±√9
x + 1 = ±3

Now solve for x:

x = -1 + 3 = 2
x = -1 - 3 = -4

Therefore, x = 2 or x = -4.