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Finite Math Examples
Step 1
To remove the radical on the left side of the equation, square both sides of the equation.
Step 2
Step 2.1
Use to rewrite as .
Step 2.2
Simplify the left side.
Step 2.2.1
Simplify .
Step 2.2.1.1
Multiply the exponents in .
Step 2.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.2.1.1.2
Cancel the common factor of .
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.
Step 2.3.1
Simplify .
Step 2.3.1.1
Rewrite as .
Step 2.3.1.2
Expand using the FOIL Method.
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.
Step 2.3.1.3.1
Simplify each term.
Step 2.3.1.3.1.1
Multiply by .
Step 2.3.1.3.1.2
Multiply by .
Step 2.3.1.3.1.3
Multiply by .
Step 2.3.1.3.1.4
Multiply .
Step 2.3.1.3.1.4.1
Raise to the power of .
Step 2.3.1.3.1.4.2
Raise to the power of .
Step 2.3.1.3.1.4.3
Use the power rule to combine exponents.
Step 2.3.1.3.1.4.4
Add and .
Step 2.3.1.3.1.5
Rewrite as .
Step 2.3.1.3.1.5.1
Use to rewrite as .
Step 2.3.1.3.1.5.2
Apply the power rule and multiply exponents, .
Step 2.3.1.3.1.5.3
Combine and .
Step 2.3.1.3.1.5.4
Cancel the common factor of .
Step 2.3.1.3.1.5.4.1
Cancel the common factor.
Step 2.3.1.3.1.5.4.2
Rewrite the expression.
Step 2.3.1.3.1.5.5
Simplify.
Step 2.3.1.3.2
Add and .
Step 3
Step 3.1
Rewrite the equation as .
Step 3.2
Move all terms not containing to the right side of the equation.
Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Subtract from both sides of the equation.
Step 3.2.3
Combine the opposite terms in .
Step 3.2.3.1
Subtract from .
Step 3.2.3.2
Add and .
Step 3.2.4
Subtract from .
Step 4
To remove the radical on the left side of the equation, square both sides of the equation.
Step 5
Step 5.1
Use to rewrite as .
Step 5.2
Simplify the left side.
Step 5.2.1
Simplify .
Step 5.2.1.1
Apply the product rule to .
Step 5.2.1.2
Use the power rule to distribute the exponent.
Step 5.2.1.2.1
Apply the product rule to .
Step 5.2.1.2.2
Apply the product rule to .
Step 5.2.1.3
Raise to the power of .
Step 5.2.1.4
Multiply the exponents in .
Step 5.2.1.4.1
Apply the power rule and multiply exponents, .
Step 5.2.1.4.2
Cancel the common factor of .
Step 5.2.1.4.2.1
Cancel the common factor.
Step 5.2.1.4.2.2
Rewrite the expression.
Step 5.2.1.5
Evaluate the exponent.
Step 5.2.1.6
Multiply by .
Step 5.2.1.7
Multiply the exponents in .
Step 5.2.1.7.1
Apply the power rule and multiply exponents, .
Step 5.2.1.7.2
Cancel the common factor of .
Step 5.2.1.7.2.1
Cancel the common factor.
Step 5.2.1.7.2.2
Rewrite the expression.
Step 5.2.1.8
Simplify.
Step 5.3
Simplify the right side.
Step 5.3.1
Simplify .
Step 5.3.1.1
Apply the product rule to .
Step 5.3.1.2
Raise to the power of .
Step 6
Step 6.1
Subtract from both sides of the equation.
Step 6.2
Factor the left side of the equation.
Step 6.2.1
Let . Substitute for all occurrences of .
Step 6.2.2
Factor out of .
Step 6.2.2.1
Factor out of .
Step 6.2.2.2
Factor out of .
Step 6.2.2.3
Factor out of .
Step 6.2.3
Replace all occurrences of with .
Step 6.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 6.4
Set equal to .
Step 6.5
Set equal to and solve for .
Step 6.5.1
Set equal to .
Step 6.5.2
Solve for .
Step 6.5.2.1
Subtract from both sides of the equation.
Step 6.5.2.2
Divide each term in by and simplify.
Step 6.5.2.2.1
Divide each term in by .
Step 6.5.2.2.2
Simplify the left side.
Step 6.5.2.2.2.1
Dividing two negative values results in a positive value.
Step 6.5.2.2.2.2
Divide by .
Step 6.5.2.2.3
Simplify the right side.
Step 6.5.2.2.3.1
Divide by .
Step 6.6
The final solution is all the values that make true.
Step 7