How do you solve using the completing the square method x^2-8x+7=0?

1 Answer
Sep 20, 2016

x=7color(white)("XX")orcolor(white)("XX")x=1

Explanation:

Given
color(white)("XXX")x^2-8x+7=0color(white)("XX")Note: I modified the question to include the color(blue)(=0)

Then
color(white)("XXX")x^2-8x=-7

Remembering the general relation:
color(white)("XXX")x^2+2ax+a^2 = (x+a)^2

If x^2-8x are to be the first two terms of x^2+2ax+a^2
then
color(white)("XXX")a=-4
and
color(white)("XXX")a^2=16

So we will need to add 16 (to both sides) to underline("complete the square")

color(white)("XXX")x^2-8x+16 = -7+16

color(white)("XXX")(x-4)^2=9

color(white)("XXX")x-4=+-3

color(white)("XXX")x=4+-3

color(white)("XXX")x=7color(white)("XX")orcolor(white)("XX")x=1