How do you complete the square to solve #2x^2 - 10x - 20 = 8#?

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Answer 1 · 2015-05-23T23:19:56

First notice that all the terms are divisible by #2#, so let us divide both sides of the equation by #2# to get:

#4=x^2-5x-10#

#= x^2-5x+25/4-25/4-10#

#= (x-5/2)^2-25/4-40/4#

#= (x-5/2)^2 - 65/4#

Add #65/4# to both ends to get:

#(x-5/2)^2 = 4+65/4 = 16/4+65/4 = 81/4 = (9/2)^2#

So

#(x-5/2) = +-9/2#

Add #5/2# to both sides to get:

#x = 5/2+-9/2#

That is #x = -4/2 = -2# or #x = 14/2 = 7#.