Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x^2 - 5x = 12
To solve this equation by completing the square, we need to add a constant term to both sides of the equation to make the left side a perfect square trinomial.
Starting with the equation: x^2 - 5x = 12
First, we take half of the coefficient of x, which is -5, and square it:
(-5/2)^2 = 25/4
Now, we add this constant term to both sides of the equation:
x^2 - 5x + 25/4 = 12 + 25/4
Combining the terms on the right side:
x^2 - 5x + 25/4 = 48/4 + 25/4
x^2 - 5x + 25/4 = 73/4
Next, we can rewrite the left side of the equation as a perfect square trinomial:
(x - 5/2)^2 = 73/4
To solve for x, we take the square root of both sides:
sqrt((x - 5/2)^2) = sqrt(73/4)
x - 5/2 = +/- sqrt(73/4)
Now we isolate x by adding 5/2 to both sides of the equation:
x = 5/2 +/- sqrt(73/4)
Finally, we can simplify the expression by multiplying the numerator and denominator of the square root by 4:
x = 5/2 +/- sqrt(73)/2
Rounded to the nearest hundredth, the solutions are:
x = 5/2 + sqrt(73)/2 ≈ 4.89
x = 5/2 - sqrt(73)/2 ≈ 0.11