Solve by completing the square.
u^2 − 14u = –33
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
To solve by completing the square, we want to rearrange the equation so that it is in the form (u - h)^2 = k.
First, add (14/2)^2 = 49 to both sides of the equation:
u^2 - 14u + 49 = -33 + 49
u^2 - 14u + 49 = 16
Now, rewrite the left side of the equation as a squared binomial:
(u - 7)^2 = 16
Now take the square root of both sides:
u - 7 = ±√16
u - 7 = ±4
Now solve for u:
u = 7 + 4 or u = 7 - 4
u = 11 or u = 3
So, the solutions to the equation u^2 − 14u = –33 are u = 11 and u = 3.