Precalculus Examples

Solve for x square root of 18x-9=x+4
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 2.3
Simplify the right side.
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Step 2.3.1
Simplify .
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Step 2.3.1.1
Rewrite as .
Step 2.3.1.2
Expand using the FOIL Method.
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Step 2.3.1.2.1
Apply the distributive property.
Step 2.3.1.2.2
Apply the distributive property.
Step 2.3.1.2.3
Apply the distributive property.
Step 2.3.1.3
Simplify and combine like terms.
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Step 2.3.1.3.1
Simplify each term.
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Step 2.3.1.3.1.1
Multiply by .
Step 2.3.1.3.1.2
Move to the left of .
Step 2.3.1.3.1.3
Multiply by .
Step 2.3.1.3.2
Add and .
Step 3
Solve for .
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Step 3.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 3.2
Move all terms containing to the left side of the equation.
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Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Subtract from .
Step 3.3
Add to both sides of the equation.
Step 3.4
Add and .
Step 3.5
Factor using the perfect square rule.
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Step 3.5.1
Rewrite as .
Step 3.5.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 3.5.3
Rewrite the polynomial.
Step 3.5.4
Factor using the perfect square trinomial rule , where and .
Step 3.6
Set the equal to .
Step 3.7
Add to both sides of the equation.