Solve by completing the square could take a little bit more time to do than solving by factoring. However, the steps are straightforward.

Before showing examples, you need to understand what a perfect square trinomial is

Binomial × same Binomial = Perfect square trinomial

(x + 4) × (x + 4) = x

(x + a) × (x + a) = x

What is the relationship between the coefficient of the second term and the last term?

For x

(8/2)

For, x

(2a/2)

So, what is the relationship?

The last term is obtained by dividing the coefficient of the second term by 2 and squaring the result

Now, let's say you have x

Just do (20/2)

Solve by completing the square x

x

Subtract 8 from both sides of the equation.

x

x

To complete the square, always do the following 24 hours a day 365 days a year. It is never going to change when you solve by completing the square!

You are basically looking for a term to add to x

To this end, get the coefficient of the second term, divide it by 2 and raise it to the second power.

The second term is 6x and the coefficient is 6.

6/2 = 3 and after squaring 3, we get 3

x

Add 3

x

x

(x + 3)

(x + 3)

Take the square root of both sides

√((x + 3)

x + 3 = ±1

When x + 3 = 1, x = -2

When x + 3 = -1, x = -4

Solve by completing the square x

The second term this time is -6x and the coefficient is -6.

-6/2 = -3 and after squaring -3, we get (-3)

x

Add (-3)

x

(x + -3)

(x + -3)

Take the square root of both sides

√((x + -3)

x + -3 = ±1

When x + -3 = 1, x = 4

When x + -3 = -1, x = 2

Solve by completing the square 3x

3x

Divide everything by 3. Always do that when the coefficient of the first term is not 1

(3/3)x

x

Add 1 to both sides of the equation.

x

x

The second term is (8/3)x and the coefficient is 8/3.

8/3 ÷ 2 = 8/3 × 1/2 = 8/6 and after squaring 8/6, we get (8/6)

x

Add (8/6)

x

(x + 8/6)

(x + 8/6)

Take the square root of both sides

√((x + 8/6)

x + 8/6 = ±10/6

x + 8/6 = 10/6

x = 10/6 - 8/6 = 2/6 = 1/3

x + 8/6 = - 10/6

x = -10/6 - 8/6 = -18/6 = -3

To solve by completing the square can become quickly hard as shwon in example #3