Finite Math Examples

Solve for x y=- square root of 49-x^2
Step 1
Rewrite the equation as .
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Reduce the expression by cancelling the common factors.
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Step 2.2.1.1
Dividing two negative values results in a positive value.
Step 2.2.1.2
Write the expression using exponents.
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Step 2.2.1.2.1
Divide by .
Step 2.2.1.2.2
Rewrite as .
Step 2.2.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2.3
Simplify the right side.
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Step 2.3.1
Move the negative one from the denominator of .
Step 2.3.2
Rewrite as .
Step 3
To remove the radical on the left side of the equation, square both sides of the equation.
Step 4
Simplify each side of the equation.
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Step 4.1
Use to rewrite as .
Step 4.2
Simplify the left side.
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Step 4.2.1
Simplify .
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Step 4.2.1.1
Multiply the exponents in .
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Step 4.2.1.1.1
Apply the power rule and multiply exponents, .
Step 4.2.1.1.2
Cancel the common factor of .
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Step 4.2.1.1.2.1
Cancel the common factor.
Step 4.2.1.1.2.2
Rewrite the expression.
Step 4.2.1.2
Expand using the FOIL Method.
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Step 4.2.1.2.1
Apply the distributive property.
Step 4.2.1.2.2
Apply the distributive property.
Step 4.2.1.2.3
Apply the distributive property.
Step 4.2.1.3
Simplify and combine like terms.
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Step 4.2.1.3.1
Simplify each term.
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Step 4.2.1.3.1.1
Multiply by .
Step 4.2.1.3.1.2
Multiply by .
Step 4.2.1.3.1.3
Move to the left of .
Step 4.2.1.3.1.4
Rewrite using the commutative property of multiplication.
Step 4.2.1.3.1.5
Multiply by by adding the exponents.
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Step 4.2.1.3.1.5.1
Move .
Step 4.2.1.3.1.5.2
Multiply by .
Step 4.2.1.3.2
Add and .
Step 4.2.1.3.3
Add and .
Step 4.2.1.4
Simplify.
Step 4.3
Simplify the right side.
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Step 4.3.1
Simplify .
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Step 4.3.1.1
Apply the product rule to .
Step 4.3.1.2
Raise to the power of .
Step 4.3.1.3
Multiply by .
Step 5
Solve for .
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Step 5.1
Subtract from both sides of the equation.
Step 5.2
Divide each term in by and simplify.
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Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
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Step 5.2.2.1
Dividing two negative values results in a positive value.
Step 5.2.2.2
Divide by .
Step 5.2.3
Simplify the right side.
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Step 5.2.3.1
Simplify each term.
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Step 5.2.3.1.1
Move the negative one from the denominator of .
Step 5.2.3.1.2
Rewrite as .
Step 5.2.3.1.3
Divide by .
Step 5.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 5.4
Simplify .
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Step 5.4.1
Simplify the expression.
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Step 5.4.1.1
Rewrite as .
Step 5.4.1.2
Reorder and .
Step 5.4.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 5.5
The complete solution is the result of both the positive and negative portions of the solution.
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Step 5.5.1
First, use the positive value of the to find the first solution.
Step 5.5.2
Next, use the negative value of the to find the second solution.
Step 5.5.3
The complete solution is the result of both the positive and negative portions of the solution.