Basic Math Examples

Solve for v (v-5)^2=2v^2-16v+33
Step 1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 2
Simplify .
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Step 2.1
Rewrite.
Step 2.2
Rewrite as .
Step 2.3
Expand using the FOIL Method.
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Step 2.3.1
Apply the distributive property.
Step 2.3.2
Apply the distributive property.
Step 2.3.3
Apply the distributive property.
Step 2.4
Simplify and combine like terms.
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Step 2.4.1
Simplify each term.
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Step 2.4.1.1
Multiply by .
Step 2.4.1.2
Move to the left of .
Step 2.4.1.3
Multiply by .
Step 2.4.2
Subtract from .
Step 3
Move all terms containing to the left side of the equation.
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Step 3.1
Subtract from both sides of the equation.
Step 3.2
Add to both sides of the equation.
Step 3.3
Subtract from .
Step 3.4
Add and .
Step 4
Subtract from both sides of the equation.
Step 5
Subtract from .
Step 6
Factor using the AC method.
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Step 6.1
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 6.2
Write the factored form using these integers.
Step 7
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 8
Set equal to and solve for .
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Step 8.1
Set equal to .
Step 8.2
Add to both sides of the equation.
Step 9
Set equal to and solve for .
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Step 9.1
Set equal to .
Step 9.2
Add to both sides of the equation.
Step 10
The final solution is all the values that make true.