Finite Math Examples

Find the Roots (Zeros) square root of 7x+1=1+ square root of 5x
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
Multiply by .
Step 2.3.1.3.1.3
Multiply by .
Step 2.3.1.3.1.4
Multiply .
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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 .
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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 .
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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
Solve for .
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Step 3.1
Rewrite the equation as .
Step 3.2
Move all terms not containing to the right 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 both sides of the equation.
Step 3.2.3
Combine the opposite terms in .
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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
Simplify each side of the equation.
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Step 5.1
Use to rewrite as .
Step 5.2
Simplify the left side.
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Step 5.2.1
Simplify .
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Step 5.2.1.1
Apply the product rule to .
Step 5.2.1.2
Use the power rule to distribute the exponent.
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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 .
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Step 5.2.1.4.1
Apply the power rule and multiply exponents, .
Step 5.2.1.4.2
Cancel the common factor of .
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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 .
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Step 5.2.1.7.1
Apply the power rule and multiply exponents, .
Step 5.2.1.7.2
Cancel the common factor of .
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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.
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Step 5.3.1
Simplify .
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Step 5.3.1.1
Apply the product rule to .
Step 5.3.1.2
Raise to the power of .
Step 6
Solve for .
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Step 6.1
Subtract from both sides of the equation.
Step 6.2
Factor the left side of the equation.
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Step 6.2.1
Let . Substitute for all occurrences of .
Step 6.2.2
Factor out of .
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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 .
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Step 6.5.1
Set equal to .
Step 6.5.2
Solve for .
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Step 6.5.2.1
Subtract from both sides of the equation.
Step 6.5.2.2
Divide each term in by and simplify.
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Step 6.5.2.2.1
Divide each term in by .
Step 6.5.2.2.2
Simplify the left side.
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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.
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Step 6.5.2.2.3.1
Divide by .
Step 6.6
The final solution is all the values that make true.
Step 7