Completing the Square Math Example 3

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

Example 3

easy
What number completes the square for x2+10x+ _ x^2 + 10x + \,\_\,?

Solution

  1. 1
    Half of 10 is 5. Square it: 52=255^2 = 25.
  2. 2
    The missing number is 25, giving (x+5)2(x + 5)^2.

Answer

2525
To complete the square for x2+bxx^2 + bx, add (b2)2(\frac{b}{2})^2.

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 1 medium

Rewrite [formula] in vertex form by completing the square.

Example 2 hard

Solve [formula] by completing the square.

Example 4 medium

Rewrite [formula] in vertex form.

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