Finite Math Examples

Find the Roots (Zeros) y=-1/2x^2+4x-6
Step 1
Set equal to .
Step 2
Solve for .
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Step 2.1
Simplify each term.
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Step 2.1.1
Move the negative in front of the fraction.
Step 2.1.2
Combine and .
Step 2.2
Multiply each term in by to eliminate the fractions.
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Step 2.2.1
Multiply each term in by .
Step 2.2.2
Simplify the left side.
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Step 2.2.2.1
Simplify each term.
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Step 2.2.2.1.1
Cancel the common factor of .
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Step 2.2.2.1.1.1
Move the leading negative in into the numerator.
Step 2.2.2.1.1.2
Cancel the common factor.
Step 2.2.2.1.1.3
Rewrite the expression.
Step 2.2.2.1.2
Multiply by .
Step 2.2.2.1.3
Multiply by .
Step 2.2.3
Simplify the right side.
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Step 2.2.3.1
Multiply by .
Step 2.3
Factor the left side of the equation.
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Step 2.3.1
Factor out of .
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Step 2.3.1.1
Factor out of .
Step 2.3.1.2
Factor out of .
Step 2.3.1.3
Rewrite as .
Step 2.3.1.4
Factor out of .
Step 2.3.1.5
Factor out of .
Step 2.3.2
Factor.
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Step 2.3.2.1
Factor using the AC method.
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Step 2.3.2.1.1
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 2.3.2.1.2
Write the factored form using these integers.
Step 2.3.2.2
Remove unnecessary parentheses.
Step 2.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.5
Set equal to and solve for .
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Step 2.5.1
Set equal to .
Step 2.5.2
Add to both sides of the equation.
Step 2.6
Set equal to and solve for .
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Step 2.6.1
Set equal to .
Step 2.6.2
Add to both sides of the equation.
Step 2.7
The final solution is all the values that make true.
Step 3