# How do you solve #x^2 - 6x + 9 = 25#?

##### 4 Answers

#### Explanation:

Given quadratic equation:

#### Explanation:

#"subtract 25 from both sides"#

#x^2-6x-16=0larrcolor(blue)"in standard form"#

#"the factors of "-16" which sum to "-6#

#"are "-8" and "+2#

#(x-8)(x+2)=0#

#"equate each factor to zero and solve for "x#

#x+2=0rArrx=-2#

#x-8=0rArrx=8#

#### Explanation:

Since we have a quadratic, let's set it equal to zero to find its zeroes. This can be done by subtracting

We now have

To factor this, let's do a little thought experiment:

What two numbers sum up to

This means we can factor this as

Setting both factors equal to zero, we get

Hope this helps!

#### Explanation:

Given:

#x^2-6x+9=25#

Note that both the left hand side and the right hand side are perfect squares, namely:

#(x-3)^2 = 5^2#

Hence:

#x-3=+-5#

So:

#x = 3+-5#

That is:

#x = 8" "# or#" "x = -2#