Algebra Examples

Solve by Factoring square root of 2x+3- square root of x+1=1
Step 1
Subtract from both sides of the equation.
Step 2
Move all terms not containing to the right side of the equation.
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Step 2.1
Add to both sides of the equation.
Step 2.2
Add to both sides of the equation.
Step 3
To remove the radical on the left side of the equation, square both sides of the equation.
Step 4
Simplify each side of the equation.
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Step 4.1
Use to rewrite as .
Step 4.2
Simplify the left side.
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Step 4.2.1
Simplify .
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Step 4.2.1.1
Multiply the exponents in .
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Step 4.2.1.1.1
Apply the power rule and multiply exponents, .
Step 4.2.1.1.2
Cancel the common factor of .
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Step 4.2.1.1.2.1
Cancel the common factor.
Step 4.2.1.1.2.2
Rewrite the expression.
Step 4.2.1.2
Simplify.
Step 4.3
Simplify the right side.
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Step 4.3.1
Simplify .
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Step 4.3.1.1
Rewrite as .
Step 4.3.1.2
Expand using the FOIL Method.
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Step 4.3.1.2.1
Apply the distributive property.
Step 4.3.1.2.2
Apply the distributive property.
Step 4.3.1.2.3
Apply the distributive property.
Step 4.3.1.3
Simplify and combine like terms.
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Step 4.3.1.3.1
Simplify each term.
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Step 4.3.1.3.1.1
Multiply .
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Step 4.3.1.3.1.1.1
Raise to the power of .
Step 4.3.1.3.1.1.2
Raise to the power of .
Step 4.3.1.3.1.1.3
Use the power rule to combine exponents.
Step 4.3.1.3.1.1.4
Add and .
Step 4.3.1.3.1.2
Rewrite as .
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Step 4.3.1.3.1.2.1
Use to rewrite as .
Step 4.3.1.3.1.2.2
Apply the power rule and multiply exponents, .
Step 4.3.1.3.1.2.3
Combine and .
Step 4.3.1.3.1.2.4
Cancel the common factor of .
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Step 4.3.1.3.1.2.4.1
Cancel the common factor.
Step 4.3.1.3.1.2.4.2
Rewrite the expression.
Step 4.3.1.3.1.2.5
Simplify.
Step 4.3.1.3.1.3
Multiply by .
Step 4.3.1.3.1.4
Multiply by .
Step 4.3.1.3.1.5
Multiply by .
Step 4.3.1.3.2
Add and .
Step 4.3.1.3.3
Add and .
Step 5
Solve for .
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Step 5.1
Rewrite the equation as .
Step 5.2
Move all terms not containing to the right side of the equation.
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Step 5.2.1
Subtract from both sides of the equation.
Step 5.2.2
Subtract from both sides of the equation.
Step 5.2.3
Subtract from .
Step 5.2.4
Subtract from .
Step 6
To remove the radical on the left side of the equation, square both sides of the equation.
Step 7
Simplify each side of the equation.
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Step 7.1
Use to rewrite as .
Step 7.2
Simplify the left side.
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Step 7.2.1
Simplify .
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Step 7.2.1.1
Apply the product rule to .
Step 7.2.1.2
Raise to the power of .
Step 7.2.1.3
Multiply the exponents in .
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Step 7.2.1.3.1
Apply the power rule and multiply exponents, .
Step 7.2.1.3.2
Cancel the common factor of .
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Step 7.2.1.3.2.1
Cancel the common factor.
Step 7.2.1.3.2.2
Rewrite the expression.
Step 7.2.1.4
Simplify.
Step 7.2.1.5
Apply the distributive property.
Step 7.2.1.6
Multiply by .
Step 7.3
Simplify the right side.
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Step 7.3.1
Simplify .
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Step 7.3.1.1
Rewrite as .
Step 7.3.1.2
Expand using the FOIL Method.
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Step 7.3.1.2.1
Apply the distributive property.
Step 7.3.1.2.2
Apply the distributive property.
Step 7.3.1.2.3
Apply the distributive property.
Step 7.3.1.3
Simplify and combine like terms.
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Step 7.3.1.3.1
Simplify each term.
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Step 7.3.1.3.1.1
Multiply by .
Step 7.3.1.3.1.2
Multiply by .
Step 7.3.1.3.1.3
Multiply by .
Step 7.3.1.3.1.4
Multiply by .
Step 7.3.1.3.2
Add and .
Step 8
Solve for .
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Step 8.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 8.2
Move all terms containing to the left side of the equation.
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Step 8.2.1
Subtract from both sides of the equation.
Step 8.2.2
Subtract from .
Step 8.3
Subtract from both sides of the equation.
Step 8.4
Subtract from .
Step 8.5
Factor using the AC method.
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Step 8.5.1
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 8.5.2
Write the factored form using these integers.
Step 8.6
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 8.7
Set equal to and solve for .
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Step 8.7.1
Set equal to .
Step 8.7.2
Add to both sides of the equation.
Step 8.8
Set equal to and solve for .
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Step 8.8.1
Set equal to .
Step 8.8.2
Subtract from both sides of the equation.
Step 8.9
The final solution is all the values that make true.