Basic Math Examples

Solve for a 1/20a^2-3/2a+10=0
Step 1
Simplify each term.
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Step 1.1
Combine and .
Step 1.2
Combine and .
Step 1.3
Move to the left of .
Step 2
Multiply each term in by to eliminate the fractions.
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Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify each term.
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Step 2.2.1.1
Cancel the common factor of .
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Step 2.2.1.1.1
Cancel the common factor.
Step 2.2.1.1.2
Rewrite the expression.
Step 2.2.1.2
Cancel the common factor of .
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Step 2.2.1.2.1
Move the leading negative in into the numerator.
Step 2.2.1.2.2
Factor out of .
Step 2.2.1.2.3
Cancel the common factor.
Step 2.2.1.2.4
Rewrite the expression.
Step 2.2.1.3
Multiply by .
Step 2.2.1.4
Multiply by .
Step 2.3
Simplify the right side.
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Step 2.3.1
Multiply by .
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
Add to both sides of the equation.
Step 7
The final solution is all the values that make true.