Precalculus Examples

Solve for x square root of x+20=x
Step 1
To remove the radical on the left side of the equation, square both sides of the equation.
Step 2
Simplify each side of the equation.
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Step 2.1
Use to rewrite as .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Multiply the exponents in .
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Step 2.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.2.1.1.2
Cancel the common factor of .
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Step 2.2.1.1.2.1
Cancel the common factor.
Step 2.2.1.1.2.2
Rewrite the expression.
Step 2.2.1.2
Simplify.
Step 3
Solve for .
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Step 3.1
Subtract from both sides of the equation.
Step 3.2
Factor the left side of the equation.
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Step 3.2.1
Factor out of .
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Step 3.2.1.1
Reorder the expression.
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Step 3.2.1.1.1
Move .
Step 3.2.1.1.2
Reorder and .
Step 3.2.1.2
Factor out of .
Step 3.2.1.3
Factor out of .
Step 3.2.1.4
Rewrite as .
Step 3.2.1.5
Factor out of .
Step 3.2.1.6
Factor out of .
Step 3.2.2
Factor.
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Step 3.2.2.1
Factor using the AC method.
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Step 3.2.2.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 3.2.2.1.2
Write the factored form using these integers.
Step 3.2.2.2
Remove unnecessary parentheses.
Step 3.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.4
Set equal to and solve for .
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Step 3.4.1
Set equal to .
Step 3.4.2
Add to both sides of the equation.
Step 3.5
Set equal to and solve for .
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Step 3.5.1
Set equal to .
Step 3.5.2
Subtract from both sides of the equation.
Step 3.6
The final solution is all the values that make true.
Step 4
Exclude the solutions that do not make true.