# How do you solve #x^2-8x+5=0#?

##### 2 Answers

We use a process called **completing the square**, which works for all quadratic equations. Here it gives

#### Explanation:

Rather than memorizing a formula, you should understand how "completing the square" works.

Render the equation as:

Then add a constant, which we will call

Now compare the left side with the identity

We then have

if

So,go back to the equation in blue and put in

So

**Root 1**

**Root 2**

#### Explanation:

**Given:**

The standard form of a quadratic is

So, we have

Solutions are given by

Using scientific calculator, we get,

**[ Intermediate Result 1 ]**

Observe that

Now, we can write **[ Intermediate Result 1 ]** as

We can rewrite the above as

Hence, we have the following two solutions:

**Root 1**

**Root 2**

Using a scientific calculator, we can simplify the above results.

**Root 1**

**Root 2**

You can verify the solutions visually by examining the image of the graph below:

Hope it helps.