Question

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

Answer 1

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`