Finite Math Examples

Solve by Substitution p=-q^2+8400 , p=50q
,
Step 1
Eliminate the equal sides of each equation and combine.
Step 2
Solve for .
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Step 2.1
Subtract from both sides of the equation.
Step 2.2
Factor the left side of the equation.
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Step 2.2.1
Factor out of .
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Step 2.2.1.1
Move .
Step 2.2.1.2
Factor out of .
Step 2.2.1.3
Factor out of .
Step 2.2.1.4
Rewrite as .
Step 2.2.1.5
Factor out of .
Step 2.2.1.6
Factor out of .
Step 2.2.2
Factor.
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Step 2.2.2.1
Factor using the AC method.
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Step 2.2.2.1.1
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 2.2.2.1.2
Write the factored form using these integers.
Step 2.2.2.2
Remove unnecessary parentheses.
Step 2.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.4
Set equal to and solve for .
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Step 2.4.1
Set equal to .
Step 2.4.2
Add to both sides of the equation.
Step 2.5
Set equal to and solve for .
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Step 2.5.1
Set equal to .
Step 2.5.2
Subtract from both sides of the equation.
Step 2.6
The final solution is all the values that make true.
Step 3
Evaluate when .
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Step 3.1
Substitute for .
Step 3.2
Multiply by .
Step 4
Evaluate when .
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Step 4.1
Substitute for .
Step 4.2
Multiply by .
Step 5
The solution of the system of equations is all the values that make the system true.
Step 6
List all of the solutions.