Pre-Algebra Examples

Solve Using the Square Root Property 7(r+3)+7(r-3)=7(r+3)(r-3)
Step 1
Simplify .
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Step 1.1
Simplify each term.
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Step 1.1.1
Apply the distributive property.
Step 1.1.2
Multiply by .
Step 1.1.3
Apply the distributive property.
Step 1.1.4
Multiply by .
Step 1.2
Simplify by adding terms.
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Step 1.2.1
Combine the opposite terms in .
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Step 1.2.1.1
Subtract from .
Step 1.2.1.2
Add and .
Step 1.2.2
Add and .
Step 2
Simplify .
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Step 2.1
Simplify by multiplying through.
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Step 2.1.1
Apply the distributive property.
Step 2.1.2
Multiply by .
Step 2.2
Expand using the FOIL Method.
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Step 2.2.1
Apply the distributive property.
Step 2.2.2
Apply the distributive property.
Step 2.2.3
Apply the distributive property.
Step 2.3
Simplify and combine like terms.
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Step 2.3.1
Simplify each term.
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Step 2.3.1.1
Multiply by by adding the exponents.
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Step 2.3.1.1.1
Move .
Step 2.3.1.1.2
Multiply by .
Step 2.3.1.2
Multiply by .
Step 2.3.1.3
Multiply by .
Step 2.3.2
Add and .
Step 2.3.3
Add and .
Step 3
Subtract from both sides of the equation.
Step 4
Add to both sides of the equation.
Step 5
Factor out of .
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Step 5.1
Reorder and .
Step 5.2
Factor out of .
Step 5.3
Factor out of .
Step 5.4
Factor out of .
Step 5.5
Factor out of .
Step 5.6
Factor out of .
Step 6
Divide each term in by and simplify.
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Step 6.1
Divide each term in by .
Step 6.2
Simplify the left side.
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Step 6.2.1
Cancel the common factor of .
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Step 6.2.1.1
Cancel the common factor.
Step 6.2.1.2
Divide by .
Step 6.3
Simplify the right side.
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Step 6.3.1
Divide by .
Step 7
Use the quadratic formula to find the solutions.
Step 8
Substitute the values , , and into the quadratic formula and solve for .
Step 9
Simplify.
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Step 9.1
Simplify the numerator.
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Step 9.1.1
Raise to the power of .
Step 9.1.2
Multiply .
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Step 9.1.2.1
Multiply by .
Step 9.1.2.2
Multiply by .
Step 9.1.3
Add and .
Step 9.1.4
Rewrite as .
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Step 9.1.4.1
Factor out of .
Step 9.1.4.2
Rewrite as .
Step 9.1.5
Pull terms out from under the radical.
Step 9.2
Multiply by .
Step 9.3
Simplify .
Step 10
Simplify the expression to solve for the portion of the .
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Step 10.1
Simplify the numerator.
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Step 10.1.1
Raise to the power of .
Step 10.1.2
Multiply .
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Step 10.1.2.1
Multiply by .
Step 10.1.2.2
Multiply by .
Step 10.1.3
Add and .
Step 10.1.4
Rewrite as .
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Step 10.1.4.1
Factor out of .
Step 10.1.4.2
Rewrite as .
Step 10.1.5
Pull terms out from under the radical.
Step 10.2
Multiply by .
Step 10.3
Simplify .
Step 10.4
Change the to .
Step 11
Simplify the expression to solve for the portion of the .
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Step 11.1
Simplify the numerator.
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Step 11.1.1
Raise to the power of .
Step 11.1.2
Multiply .
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Step 11.1.2.1
Multiply by .
Step 11.1.2.2
Multiply by .
Step 11.1.3
Add and .
Step 11.1.4
Rewrite as .
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Step 11.1.4.1
Factor out of .
Step 11.1.4.2
Rewrite as .
Step 11.1.5
Pull terms out from under the radical.
Step 11.2
Multiply by .
Step 11.3
Simplify .
Step 11.4
Change the to .
Step 12
The final answer is the combination of both solutions.
Step 13
The result can be shown in multiple forms.
Exact Form:
Decimal Form: