Question

How do you complete the square to solve `c^2 - 45c + 324 = 0`?

Answer 1

`c = 36" "` or `" "c = 9`

Explanation:

The difference of squares identity can be written:

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

Complete the square, then use this with `a=2x-45` and `b=27` as follows:

`0 = 4(c^2-45c+324)`

`color(white)(0) = 4c^2-180c+1296`

`color(white)(0) = (2c)^2-2(2c)(45)+2025-729`

`color(white)(0) = (2c-45)^2-27^2`

`color(white)(0) = ((2c-45)-27)((2c-45)+27)`

`color(white)(0) = (2c-72)(2c-18)`

`color(white)(0) = 4(c-36)(c-9)`

So:

`c = 36" "` or `" "c = 9`