# How do you solve #x^2 + 10x + 13 = 0# by completing the square?

##### 2 Answers

#### Explanation:

Given:

This process introduces an error that has to be compensated for. To do this I introduce a corrective as yet unknown value represented by

Compare to

This then written as a first step as:

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Move the square from

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Remove the

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Halve the 10

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NOW WE DETERMINE THE VALUE OF

Just for demonstration lets multiply out the brackets and then compare what we have to the original equation.

For the new equation to work we must have

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Set

Add 12 to both sides

Square root both sides

Subtract 5 from both sides

#### Explanation:

Start with

Subtract 13 from both sides:

Take 10, divide by 2, to get 5. Square 5 to get 25. Add 25 to both sides:

The left side is now a perfect square:

Now solve by taking the square root of both sides:

Subtract 5 from both sides:

Simplify the radical if you'd like: