# How do you solve using the completing the square method #3x^2+10x+13#?

##### 1 Answer

Required Solutions are

#### Explanation:

We are given the **quadratic expression**

We must use **Completing The Square Method** to find the solutions.

Let us assume that

We will find the solutions in steps.

In this step,

we will move the **constant term** to **Right-Hand Side (RHS)**

Hence, we get

**Divide each term by 3** to get the **coefficient of the #x^2# term** as

We will **add a value** to each side

In the next step, we need to figure out **how-to** find the value that goes into the

Divide the **coefficient of the ** **term** by **square it**.

The result of the calculation will replace the

The calculation is done as follows:

Coefficient of the x-term is

If we divide by 2, we will get

When we **square** this intermediate result, we get

Hence, the value

We can write the **Left-Hand-Side (LHS)** as

Note that we get the value **x-term** by

We will now work on

We will take **Square Root** on both sides to simplify:

Hence, we get

Square root and Square cancel out.

Note that, in **complex number system**,

Hence,

Hence, **required solutions** are

Hope this helps.