~ Square Root Property ~ Completing the Square ~ Quadratic Formula ~ Graphing Parabolas ~ u-Substitution ~ Polynomial Inequalities ~ Rational Inequalities ~
Solving Quadratic Equations by Completing the SquareWhen we have a quadratic that does not factor, we need a way to solve for the variable. As we saw in the "square root method", if we have a perfect square trinimial, then we have only one copy of the variable, and it is easily isolated. In the following examples, you will see how to turn any quadratic into a perfect square trinomial by "completing the square".
In this example the leading coefficient is 1, so we can begin the process of completing the square after isolating the x-terms on the left side.
To "complete the square" we must follow these steps (as long as the leading coefficient is 1):
1. take half of the x-coefficient
2. then square that new valueThe new value must be added to both sides of the equation to create a perfect square trinomial
In this example the leading coefficeint is not one, and therefore needs to be divded out first. This process often creates fractions, which makes the process of "completing the square" a little more challenging!
Every quadratic can now be solved by "completing the square". The steps are identical each time we run through the process, and therefore we can create a formula that will "complete the square" for us.
In the next section we will derive and use the Quadratic Formula to solve quadratics.
