Pre-Algebra Examples

Solve for v 2v^2+20v+51=(v+6)^2
Step 1
Simplify .
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Step 1.1
Rewrite.
Step 1.2
Rewrite as .
Step 1.3
Expand using the FOIL Method.
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Step 1.3.1
Apply the distributive property.
Step 1.3.2
Apply the distributive property.
Step 1.3.3
Apply the distributive property.
Step 1.4
Simplify and combine like terms.
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Step 1.4.1
Simplify each term.
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Step 1.4.1.1
Multiply by .
Step 1.4.1.2
Move to the left of .
Step 1.4.1.3
Multiply by .
Step 1.4.2
Add and .
Step 2
Move all terms containing to the left side of the equation.
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Step 2.1
Subtract from both sides of the equation.
Step 2.2
Subtract from both sides of the equation.
Step 2.3
Subtract from .
Step 2.4
Subtract from .
Step 3
Subtract from both sides of the equation.
Step 4
Subtract from .
Step 5
Factor using the AC method.
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Step 5.1
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 5.2
Write the factored form using these integers.
Step 6
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 7
Set equal to and solve for .
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Step 7.1
Set equal to .
Step 7.2
Subtract from both sides of the equation.
Step 8
Set equal to and solve for .
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Step 8.1
Set equal to .
Step 8.2
Subtract from both sides of the equation.
Step 9
The final solution is all the values that make true.