Finite Math Examples

Solve for t t^4-4t^3-32t^2=0
Step 1
Factor the left side of the equation.
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Step 1.1
Factor out of .
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Step 1.1.1
Factor out of .
Step 1.1.2
Factor out of .
Step 1.1.3
Factor out of .
Step 1.1.4
Factor out of .
Step 1.1.5
Factor out of .
Step 1.2
Factor.
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Step 1.2.1
Factor using the AC method.
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Step 1.2.1.1
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 1.2.1.2
Write the factored form using these integers.
Step 1.2.2
Remove unnecessary parentheses.
Step 2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3
Set equal to and solve for .
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Step 3.1
Set equal to .
Step 3.2
Solve for .
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Step 3.2.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.2.2
Simplify .
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Step 3.2.2.1
Rewrite as .
Step 3.2.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.2.2.3
Plus or minus is .
Step 4
Set equal to and solve for .
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Step 4.1
Set equal to .
Step 4.2
Add to both sides of the equation.
Step 5
Set equal to and solve for .
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Step 5.1
Set equal to .
Step 5.2
Subtract from both sides of the equation.
Step 6
The final solution is all the values that make true.