How do you solve by completing the square: #x^2=8x+10#?

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Answer 1 · 2018-07-07T07:09:42

#x = 4+- sqrt(26)#

Given: #x^2 = 8x + 10#. Solve using completing of the square.

First, group the monomials with #x# together on the same side:

#x^2 - 8x = 10#

To complete the square, multiply the constant of the #x# monomial by #1/2#: #" "-8 *1/2 = -8/2 = -4#

When you complete the square you end up adding a square term:
#(a + b)^2 = a^2 + 2ab + b^2#

#(x - 4)^2 = x^2 - 8x + color(red)( (-4)^2) #

This term must be also added to the right side of the equation:

#(x - 4)^2 = 10 + (-4)^2#

#(x-4)^2 = 26#

Square root both sides:

#x - 4 = +- sqrt(26)#

#x = 4 +- sqrt(26)#