(In this post, we’re specifically focusing on completing the square.) When you complete the square, you change the equation so that the left side of the equation is a perfect square trinomial.
Unfortunately, trying to factor this equation doesn’t result in two linear equations!īoth the quadratic formula and completing the square will let you solve any quadratic equation. Because this equation contains a non-squared $\bi x$ (in $\bo6\bi x$ ), that technique won’t work.įactoring, on the other hand, involves breaking the quadratic equation into two linear equations that are both equal to zero. Solving a quadratic equation by taking the square root involves taking the square root of each side of the equation. Unfortunately, taking the square root and factoring only work in certain situations.įor example, let’s look at the following quadratic equation: There are actually four ways to solve a quadratic equation: taking the square root, factoring, completing the square, and the quadratic formula. What Is Completing The Square and When Do You Use It? So now that you know why quadratic equations are important, let’s look at one of the most common methods of solving them: completing the square. Quadratics even fuel popular video games like Angry Birds, where the arc of each bird is calculated using the quadratic formula! Construction projects like bridges use the quadratic equation to calculate the arc of the structure, and even roller coasters use quadratics to design adrenaline-pumping tracks. Quadratic equations have all sorts of real-world applications because they're used to calculate parabolas, or arcs. (If $a$ is 0, then the equation is linear, not quadratic!) In this equation, $x$ represents an unknown number and $a$ cannot be 0.
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