# Question #e94e0

##### 3 Answers

#### Explanation:

#color(blue)(r^2=-14+9r#

Bring everything to the left hand side

Now, this is a quadratic equation. Solve it by using the Quadratic formula

#color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)#

Where

Now, there are two solutions for

#color(purple)(r=(9+5)/2=14/2=7)#

#color(violet)(r=(9-5)/2=4/2=2)#

Hope this helps..! :)

#### Explanation:

Re-arrange it into general form first:

It does not matter at all what the variable is!

This means:

The quadratic formula is:

Use the values for

There are two possible answers for

We could also have solved the original equation by finding the factors.

#### Explanation:

#"rearrange and equate to zero"#

#rArrr^2-9r+14=0#

#"compare to the standard form " ax^2+bx+c=0#

#"here " a=1, b=-9, c=14#

#rArrr=(-b+-sqrt(b^2-4ac))/(2a)#

#color(white)(rArrr)=(-(-9)+-sqrt((-9)^2-(4xx1xx14)))/2#

#color(white)(rArrr)=(9+-sqrt(81-56))/2=(9+-sqrt25)/2#

#rArrr=(9+5)/2=7" or " r=(9-5)/2=2#