Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x2 – 6x = –8
To solve this equation by completing the square, we need to rearrange the terms:
x^2 - 6x = -8
x^2 - 6x + 9 = -8 + 9 (Adding (6/2)^2 = 9 to both sides to complete the square)
(x - 3)^2 = 1
Now, take the square root of both sides to solve for x:
x - 3 = ±√1
x - 3 = ±1
x = 3 ± 1
So x can be:
x = 3 + 1 = 4
x = 3 - 1 = 2
Therefore, the solutions to the equation are x = 4 and x = 2.