Solving Quadratic Equations by Completing the Square

Completing the Square

This post talks about solving quadratic equation by method of completing the square - though we know that quadratic equations can be solved by different methods.

Skills needed: Knowledge in the following methods:

• Extracting Square Root
• Factoring Method

Also, recall on the following property:

• Square-Root Property

• Zero Product Property

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There are some quadratic equations that cannot be solved by factoring , therefore it is very important that you know well on how to extract square root since it is part of the process in completing the square.

Let us review on the method where equations of the form is solved by the square root property.

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Let us consider the following equation:

The equation can be solved in a similar way since the left side of the equation is a perfect square trionomial.

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What to do if equation is non-factorable quadratic trinomial?

To solve quadratic equations by taking the square root, you must have a perfect square equal to a constant. A non-factorable quadratic trinomial should be changed to a perfect square trinomial and that is what we called completing the square.

How to change a non-factorable quadratic trinomial to a perfect square trinomial?

The following is an example of a perfect square.

Notice that the square of half of the middle coefficient is the last term.

Let us take the equation . We have to rewrite this equation in the form of so that we can use the square root property.

These are the Steps in Solving Quadratic Equation by Completing the Square

Solve

Let's check if our answer is correct:

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How about if (a) is not equal to 1?

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Summary of the steps in solving quadratic equation by completing the square:

1. Rewrite the equation If a ≠ 1 divide both sides of the equation by a.

2. Take half the coefficient of the x – term and square the result. Add the square to both sides of the equation.

3. Factor the left side of the equation and simplify the right side.

4. Apply the square root property.

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Now try this!

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for a job well done!

Steem on!
Yours Trully,

@fabio2614