# How do you solve #(c - 3) ( c - 1) = 6#?

##### 2 Answers

#### Explanation:

First we can put the equation into standard form

Since you can't factor this polynomial, we can use the quadratic formula

In this case

and we replace

then we plug in

Since

Which means that

Complete the square to find:

#c = 2+sqrt(7)" "# or#" "c = 2 - sqrt(7)#

#### Explanation:

The difference of squares identity can be written:

#a^2-b^2 = (a-b)(a+b)#

We can use this with

Given:

#(c-3)(c-1) = 6#

Multiply out the left hand side to get:

#c^2-4c+3 = 6#

Subtract

#c^2-4c-3 = 0#

Complete the square and use the difference of squares identity to find:

#0 = c^2-4c-3#

#color(white)(0) = c^2-4c+4-7#

#color(white)(0) = (c-2)^2-(sqrt(7))^2#

#color(white)(0) = ((c-2)-sqrt(7))((c-2)+sqrt(7))#

#color(white)(0) = (c-2-sqrt(7))(c-2+sqrt(7))#

Hence:

#c = 2+sqrt(7)" "# or#" "c = 2 - sqrt(7)#