How do you solve using the completing the square method #4v^2+ 16v=65#?

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Answer 1 · 2016-05-20T14:48:55

Follow the steps below to get to #v=-2+9/2=5/2#,
#v=-2-9/2=-13/2#

To complete the square, we first want the set up we have in this problem, that is v terms on one side and the constant on the other.

So first we want a clean #v^2# term, so we'll divide through by its coefficient:

#4v^2+16v=65#

#v^2+4v=65/4#

Now we take the #v# coefficient, divide by 2, then square it and add it to both sides:

#(4/2)^2=2^2=4#

#v^2+4v+4=65/4+4#

Now we convert the left side of the equation to a square (and simplify the right):

#(v+2)^2=65/4+16/4=81/4#

Now take the square root of both sides:

#v+2=+-sqrt(81/4)=+-9/2#

And finally solve for #v#:

#v=-2+-9/2#

#v=-2+9/2=5/2#
#v=-2-9/2=-13/2#