SOLUTION: |x − 11| = x2 − 11x

Question 708291: |x − 11| = x2 − 11x
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

If this were

would it be easier? You probably know that this would be solved using two equations:
or

Well, the problem we have can be solved in exactly the same way!
or
The trick part is that we need the negative of the whole right side in the second equation. When the right side is just a number, like 35, you can just stick a "-" in front. But with multiple terms, like , we need to put parentheses around the right side. With the parentheses, the "-" in front will negate the entire expression, not just the .

We now have two quadratic equations to solve. Let's do them one at a time. With the first equation we want one side to be zero. Subtracting the entire left side from both sides we get:

This will not factor we we will use the Quadratic Formula:

Simplifying...

which is short for:
or

Now for the second equation we got earlier:

Before we get the zero, let's simplify the right side:

Adding and subtracting 11x we get:

Again this will not factor so again we use the formula:

Simplifying...

which is short for:
or

So there are four solutions to your equation:
or
or
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SOLUTION: |x &#8722; 11| = x2 &#8722; 11x

SOLUTION: |x − 11| = x2 − 11x