How do you solve the equation #x^2-10x+25=49# by completing the square?
1 Answer
Dec 13, 2016
Explanation:
The difference of squares identity can be written:
#a^2-b^2 = (a-b)(a+b)#
Use this with
Given:
#x^2-10x+25=49#
Both sides of this equation are already perfect squares:
#(x-5)^2 = x^2-10x+25 = 49 = 7^2#
Subtract
#0 = (x-5)^2-7^2 = ((x-5)-7)((x-5)+7) = (x-12)(x+2)#
Hence:
#x=12" "# or#" "x = -2#