Find the roots of the polynomial by completing the square.
First, we want to find the two solutions of the equation
Divide by the leading term 2:
Transfer the constant term to the other side:
We complete the square by adding 25/16 on both sides, since we will exploit the binomial formula
Our equation now reads as:
Take square roots:
and solve for x:
Our two roots are
Consequently the polynomial can be factored as
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