Completing the Square Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

medium
Rewrite x2+6x+2x^2 + 6x + 2 in vertex form by completing the square.

Solution

  1. 1
    Take half of the coefficient of xx: 62=3\frac{6}{2} = 3.
  2. 2
    Square it: 32=93^2 = 9.
  3. 3
    Add and subtract 9: x2+6x+9−9+2=(x+3)2−7x^2 + 6x + 9 - 9 + 2 = (x + 3)^2 - 7.

Answer

(x+3)2−7(x + 3)^2 - 7
Completing the square transforms a quadratic into vertex form a(x−h)2+ka(x-h)^2 + k by creating a perfect square trinomial. The vertex is (−3,−7)(-3, -7).

About Completing the Square

A technique for rewriting ax2+bx+cax^2 + bx + c in vertex form a(x−h)2+ka(x - h)^2 + k by adding and subtracting the value (b2a)2\left(\frac{b}{2a}\right)^2 to create a perfect square trinomial.

Learn more about Completing the Square →

More Completing the Square Examples

Example 2 hard

Solve [formula] by completing the square.

Example 3 easy

What number completes the square for [formula]?

Example 4 medium

Rewrite [formula] in vertex form.

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