Solve Quadratic Equations by Square Roots

Often the easiest way to solve a quadratic equation is by taking the square root of both side of the equation (as illustrated below).   Now this method of taking the square roots of  both sides is only practical when it results in getting the variable by itself on one side of the equation.  So we can’t use the method in every problem however when you can use it you should.  Let’s take a look at the main steps involved in this excellent technique.   First you need to isolate the “x squared” part of the equation- just do the same steps as if you were trying to solve for x however you will be solving for “x squared”.  The last step is taking the square root of both sides and simplifying the result to get your two solutions (remember quadratic equations will always have two solutions).   So, keep on the look out for quadratic equations where you can solve by taking the square roots it will make your algebra work a little easier!

some key topics that involve solving quadratic equations by square roots:

* polynomial equations
* completing the square
* rational equations
* radical equations
* quadratic inequalities
* SAT and ACT exams
* college prep math and science courses




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