Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x^2- 5x= 12
To complete the square, we need to add a constant term to both sides of the equation.
First, let's move the constant term to the other side:
x^2 - 5x - 12 = 0
Now, we need to find the constant term that, when added to both sides, will allow us to create a perfect square trinomial on the left side. To do this, we take half of the coefficient of x (in this case, -5) and square it:
(-5/2)^2 = 25/4
So, we need to add 25/4 to both sides of the equation:
x^2 - 5x + 25/4 = 12 + 25/4
x^2 - 5x + 25/4 = 48/4 + 25/4
x^2 - 5x + 25/4 = 73/4
Now, let's express the left side as a perfect square:
(x - 5/2)^2 = 73/4
To solve for x, we take the square root of both sides:
√((x - 5/2)^2) = √(73/4)
x - 5/2 = ±√(73/4)
Now, let's solve for x by adding 5/2 to both sides:
x = 5/2 ± √(73/4)
To round to the nearest hundredth, we get:
x ≈ 5/2 ± √(73/4) ≈ 3.79 or 6.21