Finite Math Examples

Solve by Factoring x^2+(x+10)^2=(x+20)^2
Step 1
Subtract from both sides of the equation.
Step 2
Simplify .
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Step 2.1
Simplify each term.
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Step 2.1.1
Rewrite as .
Step 2.1.2
Expand using the FOIL Method.
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Step 2.1.2.1
Apply the distributive property.
Step 2.1.2.2
Apply the distributive property.
Step 2.1.2.3
Apply the distributive property.
Step 2.1.3
Simplify and combine like terms.
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Step 2.1.3.1
Simplify each term.
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Step 2.1.3.1.1
Multiply by .
Step 2.1.3.1.2
Move to the left of .
Step 2.1.3.1.3
Multiply by .
Step 2.1.3.2
Add and .
Step 2.1.4
Rewrite as .
Step 2.1.5
Expand using the FOIL Method.
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Step 2.1.5.1
Apply the distributive property.
Step 2.1.5.2
Apply the distributive property.
Step 2.1.5.3
Apply the distributive property.
Step 2.1.6
Simplify and combine like terms.
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Step 2.1.6.1
Simplify each term.
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Step 2.1.6.1.1
Multiply by .
Step 2.1.6.1.2
Move to the left of .
Step 2.1.6.1.3
Multiply by .
Step 2.1.6.2
Add and .
Step 2.1.7
Apply the distributive property.
Step 2.1.8
Simplify.
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Step 2.1.8.1
Multiply by .
Step 2.1.8.2
Multiply by .
Step 2.2
Combine the opposite terms in .
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Step 2.2.1
Subtract from .
Step 2.2.2
Add and .
Step 2.3
Subtract from .
Step 2.4
Subtract from .
Step 3
Factor using the AC method.
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Step 3.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 3.2
Write the factored form using these integers.
Step 4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 5
Set equal to and solve for .
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Step 5.1
Set equal to .
Step 5.2
Add to both sides of the equation.
Step 6
Set equal to and solve for .
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Step 6.1
Set equal to .
Step 6.2
Subtract from both sides of the equation.
Step 7
The final solution is all the values that make true.