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

1 Answer
Feb 26, 2017

Answer:

#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#