How do you complete the square to solve #c^2 - 45c + 324 = 0#?
1 Answer
Feb 26, 2017
Explanation:
The difference of squares identity can be written:
#a^2-b^2 = (a-b)(a+b)#
Complete the square, then use this with
#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#
