Finite Math Examples

Solve for x (x^2-6x)^2-2(x^2-6x)-35=0
Step 1
Factor the left side of the equation.
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Step 1.1
Let . Substitute for all occurrences of .
Step 1.2
Factor using the AC method.
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Step 1.2.1
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 1.2.2
Write the factored form using these integers.
Step 1.3
Replace all occurrences of with .
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
Factor using the AC method.
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Step 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 3.2.1.2
Write the factored form using these integers.
Step 3.2.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.2.3
Set equal to and solve for .
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Step 3.2.3.1
Set equal to .
Step 3.2.3.2
Add to both sides of the equation.
Step 3.2.4
Set equal to and solve for .
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Step 3.2.4.1
Set equal to .
Step 3.2.4.2
Subtract from both sides of the equation.
Step 3.2.5
The final solution is all the values that make true.
Step 4
Set equal to and solve for .
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Step 4.1
Set equal to .
Step 4.2
Solve for .
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Step 4.2.1
Factor using the AC method.
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Step 4.2.1.1
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 4.2.1.2
Write the factored form using these integers.
Step 4.2.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.2.3
Set equal to and solve for .
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Step 4.2.3.1
Set equal to .
Step 4.2.3.2
Add to both sides of the equation.
Step 4.2.4
Set equal to and solve for .
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Step 4.2.4.1
Set equal to .
Step 4.2.4.2
Add to both sides of the equation.
Step 4.2.5
The final solution is all the values that make true.
Step 5
The final solution is all the values that make true.