Useful Tips to Complete The Square in Math

Here you will be writing a quadratic in completed square form. For example, Complete the square on this quadratic equation x² + 5x + 4.

In this article we shall be writing a quadratic equation that has the form x² + bx + c in the form (x + m)² + n (completed square form where m and n are values which need to be worked out).  The examples shown below are quite difficult so if you need to see easier examples on completing the square then read here first.

Question A

Complete the square on this quadratic equation x² + 5x + 4.

So what you need to do is write the quadratic in the form (x+m)² + n. Also b = 5 and c =4.

Step 1: Divide the number before x by 2 to give m

m = b/2

m=5/2

Leaving this as an improper fraction will be fine but you can write it as a decimal if you prefer.

Step 2: Square the value you have just work out and take this away from c.

n = c – m²

n = 4 – (5/2)²

n = 4 – 25/4

n = 16/4 – 25/4

n= -9/4

Step 3: Plug these numbers back into completed square form.

So (x+5/2)² -9/4

Question B

Complete the square on this quadratic equation x² -3x – 2.

So what you need to do is write the quadratic in the form (x+m)² + n. Also b = -3 and c = -2.

Step 1: Divide the number before x by 2 to give m

m = b/2

m=-3/2

Leaving this as an improper fraction will be fine but you can write it as a decimal if you prefer.

Step 2: Square the value you have just work out and take this away from c.

n = c – m²

n = -2 – (-3/2)²

n = -2 – 9/4

n = -8/4 – 9/4

n= -17/4

Step 3: Plug these numbers back into completed square form.

So (x – 3/2)² -17/4

If you are still finding these examples tough then read some more theory on completing the square by clicking here.

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