Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x^2 - 2x = 24

Answer 1

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.