Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x^2 - 2x = 24
To solve the equation by completing the square, we need to rearrange it so that the left side is a perfect square trinomial.
To do that, we can add the square of half the coefficient of x to both sides of the equation.
Starting with x^2 - 2x = 24, we can add (-2/2)^2 = 1 to both sides:
x^2 - 2x + 1 = 24 + 1
x^2 - 2x + 1 = 25
Now, we can rewrite the left side as a perfect square trinomial:
(x - 1)^2 = 25
Taking the square root of both sides, we get:
x - 1 = ±√25
Simplifying, we have:
x - 1 = ±5
Now, we can solve for x by adding 1 to both sides:
x = 1 ± 5
This gives us two possible solutions:
x = 1 + 5 = 6
x = 1 - 5 = -4
Therefore, the solutions to the equation x^2 - 2x = 24 are x = 6 and x = -4.