# Solving quadratic equations by factoring method

## Solve the equation below step-by-step by **factoring method**

Solving equations using factoring method is a daunting task as you have to carefully look for numbers that will produce roots of the quadratic equation.

**Steps of factoring method**

- Put all terms in one side preferably the left side and put zero on one side preferably right side
- Arrange the terms in the general form of quadratic equation
- Find product of first and third term
- Find two numbers or factors when multiplied they give the product in step 3. above and when added they give the second term
- Rewrite the equation and substitute the middle term with the two factors you found in step 4.
- Group and factorise the first two terms and last two terms
- Find common linear factor, factorise further and completely
- Equate each linear factor to zero
- Obtain the roots

Find product of first and third term

Find factors that give the product above; when added they give the sum of middle term

Sum of factors that equal second term

The factors summed up in this case are generated from testing various divisors of

**Completing the square method**

## Let’s start

Let’s switch off from factoring method to completing the square method and see how beautifully the equation is solved.

This is a quadratic equation of the form

Divide by **6 **throughout to make the coefficient of** x **squared ** 1**

In order to complete the square, take half the coefficient of **x** in the second term, square the result and add to both sides

To make **LHS** a perfect square express in the form of

On the RHS find the **LCM** of the fractions and add them together. In this case the **LCM** is **144**

As you can see the **RHS** is simplified

Take the square roots on both sides

Taking square roots results in two solutions denoted by **±**

Find values of **x** by adding the constant terms on the **LHS** to both sides

Separate into two equations and simplify them by addition or subtraction

Find the **LCM** and get the results as shown below. Since the denominators are the same in both cases ( **6 **and **12** ), the **LCM** is **12**

Therefore,

Or

That is it!