Pre-Algebra Examples

Solve Using the Square Root Property (3x+5)(x-5)=-2x(6x+5)+x-19
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
Simplify each term.
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Step 2.1.1
Apply the distributive property.
Step 2.1.2
Rewrite using the commutative property of multiplication.
Step 2.1.3
Multiply by .
Step 2.1.4
Simplify each term.
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Step 2.1.4.1
Multiply by by adding the exponents.
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Step 2.1.4.1.1
Move .
Step 2.1.4.1.2
Multiply by .
Step 2.1.4.2
Multiply by .
Step 2.2
Add and .
Step 3
Simplify .
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Step 3.1
Expand using the FOIL Method.
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Step 3.1.1
Apply the distributive property.
Step 3.1.2
Apply the distributive property.
Step 3.1.3
Apply the distributive property.
Step 3.2
Simplify and combine like terms.
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Step 3.2.1
Simplify each term.
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Step 3.2.1.1
Multiply by by adding the exponents.
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Step 3.2.1.1.1
Move .
Step 3.2.1.1.2
Multiply by .
Step 3.2.1.2
Multiply by .
Step 3.2.1.3
Multiply by .
Step 3.2.2
Add and .
Step 4
Move all terms containing to the left side of the equation.
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Add to both sides of the equation.
Step 4.3
Subtract from .
Step 4.4
Add and .
Step 5
Add to both sides of the equation.
Step 6
Add and .
Step 7
Factor the left side of the equation.
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Step 7.1
Factor out of .
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Step 7.1.1
Factor out of .
Step 7.1.2
Factor out of .
Step 7.1.3
Rewrite as .
Step 7.1.4
Factor out of .
Step 7.1.5
Factor out of .
Step 7.2
Factor.
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Step 7.2.1
Factor by grouping.
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Step 7.2.1.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 7.2.1.1.1
Factor out of .
Step 7.2.1.1.2
Rewrite as plus
Step 7.2.1.1.3
Apply the distributive property.
Step 7.2.1.2
Factor out the greatest common factor from each group.
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Step 7.2.1.2.1
Group the first two terms and the last two terms.
Step 7.2.1.2.2
Factor out the greatest common factor (GCF) from each group.
Step 7.2.1.3
Factor the polynomial by factoring out the greatest common factor, .
Step 7.2.2
Remove unnecessary parentheses.
Step 8
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 9
Set equal to and solve for .
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Step 9.1
Set equal to .
Step 9.2
Solve for .
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Step 9.2.1
Subtract from both sides of the equation.
Step 9.2.2
Divide each term in by and simplify.
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Step 9.2.2.1
Divide each term in by .
Step 9.2.2.2
Simplify the left side.
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Step 9.2.2.2.1
Cancel the common factor of .
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Step 9.2.2.2.1.1
Cancel the common factor.
Step 9.2.2.2.1.2
Divide by .
Step 9.2.2.3
Simplify the right side.
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Step 9.2.2.3.1
Move the negative in front of the fraction.
Step 10
Set equal to and solve for .
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Step 10.1
Set equal to .
Step 10.2
Solve for .
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Step 10.2.1
Add to both sides of the equation.
Step 10.2.2
Divide each term in by and simplify.
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Step 10.2.2.1
Divide each term in by .
Step 10.2.2.2
Simplify the left side.
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Step 10.2.2.2.1
Cancel the common factor of .
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Step 10.2.2.2.1.1
Cancel the common factor.
Step 10.2.2.2.1.2
Divide by .
Step 11
The final solution is all the values that make true.