How do you complete the square to solve c^2 - 45c + 324 = 0c2−45c+324=0?
1 Answer
Feb 26, 2017
Explanation:
The difference of squares identity can be written:
a^2-b^2 = (a-b)(a+b)a2−b2=(a−b)(a+b)
Complete the square, then use this with
0 = 4(c^2-45c+324)0=4(c2−45c+324)
color(white)(0) = 4c^2-180c+12960=4c2−180c+1296
color(white)(0) = (2c)^2-2(2c)(45)+2025-7290=(2c)2−2(2c)(45)+2025−729
color(white)(0) = (2c-45)^2-27^20=(2c−45)2−272
color(white)(0) = ((2c-45)-27)((2c-45)+27)0=((2c−45)−27)((2c−45)+27)
color(white)(0) = (2c-72)(2c-18)0=(2c−72)(2c−18)
color(white)(0) = 4(c-36)(c-9)0=4(c−36)(c−9)
So:
c = 36" "c=36 or" "c = 9 c=9
