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Why is it necessary to check your solutions when solving a rational equation?

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It is always important to check your answers.

For example you have the following problem:

If you have x quarters, your mom has 25 quarters. The amount of quarters you have raised to the power of 2 is equal to the amount of quarters your mom has.  How many quarters do you have?

the equation is x^2=25.  Well x is = to +5 & -5, because 5*5=25 & -5*-5=25.

But you can not have -5 quarters. So you need to check your solutions to make sure they make sense.