FSQE - Solve Quadratics by Completing the Square (Lesson)

Solve Quadratics by Completing the Square

The last method of solving we will learn is completing the square.

In order to understand how to complete the square, you must first understand what is a perfect square trinomial. Perfect square trinomials have specific factoring patterns. Here are a few examples:

See if you can figure out the pattern of creating a perfect square trinomial and try the matching problems below:

Now let's try to solve by completing the square:

Start with an equation in standard form and add or subtract the c value to the other side. The leading coefficient (or "a") needs to be a 1. If the leading coefficient is a number other than 1, divide through by that value.

x² + 8x + 1 = 0

x² + 8x = -1

Determine what value will make a "perfect square trinomial" and add that to both sides.
Hint: If you are having a hard time figuring it out, there is a formula and it is (b/2)²

x² + 8x + ___ = -1 + ___

x² + 8x + 16 = -1 + 16

Now factor the left side and simplify the right side.

(x + 4)² = 15

Solve by taking square roots.

$x+4=\pm\sqrt[2]{15}$ 

$x=-4\pm\sqrt[2]{15}$ 

Note: The method of "completing the square" is how mathematicians developed the quadratic formula.

Watch this video to see more examples of solving by completing the square.

Now try these to see if you've got it. Give answers for #1-2 in exact form and #3 in approximate form:

Solve Quadratics by Completing the Square Practice

1. x² + 10x = 7
2. x² = 20x + 20
3. x² - 6x - 39 =0

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

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