Solve the equation by completing the square. Round to the nearest hundredth if necessary.

Question

x2 + 2x = 8
(1 point)
Responses

x = 2, 4
x = 2, 4

x = –2, 4
x = –2, 4

x = 2, –4
x = 2, –4

x = –2, –4

Answer 1

x^2 + 2x = 8

To complete the square, first add and subtract (2/2)^2 = 1 to both sides:

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

Now we take the square root of both sides:

x + 1 = ±√9
x + 1 = ±3

Solve for x:

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

Therefore, the solutions are x = 2 and x = -4.

So x = 2 and x = -4.