Pre-Algebra Examples

Solve Using the Square Root Property 36=1/2*((x+2)(x+8))
Step 1
Rewrite the equation as .
Step 2
Multiply both sides of the equation by .
Step 3
Simplify both sides of the equation.
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Step 3.1
Simplify the left side.
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Step 3.1.1
Simplify .
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Step 3.1.1.1
Expand using the FOIL Method.
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Step 3.1.1.1.1
Apply the distributive property.
Step 3.1.1.1.2
Apply the distributive property.
Step 3.1.1.1.3
Apply the distributive property.
Step 3.1.1.2
Simplify and combine like terms.
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Step 3.1.1.2.1
Simplify each term.
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Step 3.1.1.2.1.1
Multiply by .
Step 3.1.1.2.1.2
Move to the left of .
Step 3.1.1.2.1.3
Multiply by .
Step 3.1.1.2.2
Add and .
Step 3.1.1.3
Apply the distributive property.
Step 3.1.1.4
Simplify.
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Step 3.1.1.4.1
Combine and .
Step 3.1.1.4.2
Cancel the common factor of .
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Step 3.1.1.4.2.1
Factor out of .
Step 3.1.1.4.2.2
Cancel the common factor.
Step 3.1.1.4.2.3
Rewrite the expression.
Step 3.1.1.4.3
Cancel the common factor of .
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Step 3.1.1.4.3.1
Factor out of .
Step 3.1.1.4.3.2
Cancel the common factor.
Step 3.1.1.4.3.3
Rewrite the expression.
Step 3.1.1.5
Apply the distributive property.
Step 3.1.1.6
Simplify.
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Step 3.1.1.6.1
Cancel the common factor of .
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Step 3.1.1.6.1.1
Cancel the common factor.
Step 3.1.1.6.1.2
Rewrite the expression.
Step 3.1.1.6.2
Multiply by .
Step 3.1.1.6.3
Multiply by .
Step 3.2
Simplify the right side.
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Step 3.2.1
Multiply by .
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
Subtract from both sides of the equation.
Step 10
The final solution is all the values that make true.