Finite Math Examples

Solve by Factoring 16n^2=49
Step 1
Subtract from both sides of the equation.
Step 2
Rewrite as .
Step 3
Rewrite as .
Step 4
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 5
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 6
Set equal to and solve for .
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Step 6.1
Set equal to .
Step 6.2
Solve for .
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Step 6.2.1
Subtract from both sides of the equation.
Step 6.2.2
Divide each term in by and simplify.
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Step 6.2.2.1
Divide each term in by .
Step 6.2.2.2
Simplify the left side.
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Step 6.2.2.2.1
Cancel the common factor of .
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Step 6.2.2.2.1.1
Cancel the common factor.
Step 6.2.2.2.1.2
Divide by .
Step 6.2.2.3
Simplify the right side.
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Step 6.2.2.3.1
Move the negative in front of the fraction.
Step 7
Set equal to and solve for .
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Step 7.1
Set equal to .
Step 7.2
Solve for .
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Step 7.2.1
Add to both sides of the equation.
Step 7.2.2
Divide each term in by and simplify.
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Step 7.2.2.1
Divide each term in by .
Step 7.2.2.2
Simplify the left side.
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Step 7.2.2.2.1
Cancel the common factor of .
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Step 7.2.2.2.1.1
Cancel the common factor.
Step 7.2.2.2.1.2
Divide by .
Step 8
The final solution is all the values that make true.