Completing the Square, Answer 2

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:

Simplify:

Take square roots:

and solve for x:

Our two roots are

Consequently the polynomial can be factored as

2 displaymath73

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Helmut Knaust
Sat Jun 21 21:01:03 MDT 1997