# How do you solve #x^2+3x+21=22# by completing the square?

##### 2 Answers

#### Explanation:

Steps:

Subtract 21 from both sides

In order to find ?, you must divide

Now we can factor the left side and simplify the right.

Finally, solve for

#### Explanation:

Squares of form

#x^2 + 2ax + a^2#

Since our equation starts with

To do this, we can subtract

#color(white)"X"x^2 + 3x + 21 = 22#

#color(white)"X" x^2 + 3x + 9/4 = 13/4#

#color(white)"XX.." (x + 1.5)^2 = 13/4#

Now we can take the square root of both sides. Remember that the square root can be either positive or negative, since when squared, the negative sign disappears.

#color(white)"" x + 3/2 = +- sqrt13/2#

#color(white)"XXX." x = (-3 +- sqrt13)/2#

*Final Answer*