# How do you solve #x^2-5x-6=0# by completing the square?

##### 2 Answers

Please do not change this solution. It is a reference solution.

#### Explanation:

Given the standard form

We end up with form

The problem is that changing the original equation to this form introduces an error. So

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Given:

Write as:

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Move the power from

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Discard the

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Halve the 5 inside the brackets

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Determine the value of

Let

So by substitution equation(2) becomes:

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Using

Vertex

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Add

Square root both sides

Add

As Tony B. states the answer is

#### Explanation:

In this method a different approach is used to complete the square. The idea is to show more clearly how the coefficient

Start with the expression

These expression is the same as the first two terms of the quadratic expression originally given. We render this as a difference of squares:

And then we match the two sets of factors:

Now add these two equations together and note that in eliminating

Then take the difference of the original two equations to get

This works because the original quadratic expression had a coefficient of

Then we have:

And the original equation becomes:

So we take both possible square roots noting that

If we did not have a perfect square the final answer would contain square roots.