How do you solve the equation #2x^2+10x+1=13# by completing the square?

1 Answer
Y
May 7, 2017

Put constants on one side and x terms on the other side and complete the square.

Explanation:

By subtracting 1 from both sides, we get:
#2x^2+10x=12#
We can simplify by dividing both sides by 2:
#x^2+5x=6#
Here we complete the square:
Since #(a+b)^2=a^2+2ab+b^2#, here #a^2# is #x^2# and our #2ab# term is #5x#, therefore our #b# term must be #5/2#. We complete the square by making #x^2+5x# into the form of the #(a+b)^2#, however we also need to subtract the #b^2# term since we had added it in to complete the square:
#(x^2+5x+(5/2)^2)-(5/2)^2=6#
#(x+5/2)^2-25/4=6#
and simplify:
#(x+5/2)^2=49/4#
#x+5/2=+-sqrt(49/4)#
#x+5/2=+-7/2#
#x=(-5+-7)/2#
#x=-6 or x=1#

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