How do you solve the equation #x^2+1.4x+0.49=0.81# by completing the square?
1 Answer
Dec 18, 2016
Explanation:
We will use the difference of squares identity, which can be written:
#a^2-b^2 = (a-b)(a+b)#
Given:
#x^2+1.4x+0.49 = 0.81#
Both the left hand and right hand side of this equation are perfect squares already:
#(x+0.7^2) = x^2+1.4x+0.49 = 0.81 = 0.9^2#
Hence:
#0 = (x+0.7^2)-0.9^2#
#color(white)(0) = ((x+0.7)-0.9)((x+0.7)+0.9)#
#color(white)(0) = (x-0.2)(x+1.6)#
Hence:
#x = 0.2" "# or#" "x = -1.6#