Question

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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.