Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 + 2x = 8
x=2,4
x=-2,4
x=2, -4
x= -2 , -4
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.