Pre-Algebra Examples

Solve Using the Square Root Property 38x^2+4x+13=27x^2+4x+4
Step 1
Move all terms containing to the left side of the equation.
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Step 1.1
Subtract from both sides of the equation.
Step 1.2
Subtract from both sides of the equation.
Step 1.3
Combine the opposite terms in .
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Step 1.3.1
Subtract from .
Step 1.3.2
Add and .
Step 1.4
Subtract from .
Step 2
Move all terms not containing to the right side of the equation.
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Step 2.1
Subtract from both sides of the equation.
Step 2.2
Subtract from .
Step 3
Divide each term in by and simplify.
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Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Cancel the common factor of .
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Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Divide by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Move the negative in front of the fraction.
Step 4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 5
Simplify .
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Step 5.1
Rewrite as .
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Step 5.1.1
Rewrite as .
Step 5.1.2
Rewrite as .
Step 5.2
Pull terms out from under the radical.
Step 5.3
Raise to the power of .
Step 5.4
Rewrite as .
Step 5.5
Simplify the numerator.
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Step 5.5.1
Rewrite as .
Step 5.5.2
Pull terms out from under the radical, assuming positive real numbers.
Step 5.6
Multiply by .
Step 5.7
Combine and simplify the denominator.
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Step 5.7.1
Multiply by .
Step 5.7.2
Raise to the power of .
Step 5.7.3
Raise to the power of .
Step 5.7.4
Use the power rule to combine exponents.
Step 5.7.5
Add and .
Step 5.7.6
Rewrite as .
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Step 5.7.6.1
Use to rewrite as .
Step 5.7.6.2
Apply the power rule and multiply exponents, .
Step 5.7.6.3
Combine and .
Step 5.7.6.4
Cancel the common factor of .
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Step 5.7.6.4.1
Cancel the common factor.
Step 5.7.6.4.2
Rewrite the expression.
Step 5.7.6.5
Evaluate the exponent.
Step 5.8
Combine and .
Step 5.9
Move to the left of .
Step 6
The complete solution is the result of both the positive and negative portions of the solution.
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Step 6.1
First, use the positive value of the to find the first solution.
Step 6.2
Next, use the negative value of the to find the second solution.
Step 6.3
The complete solution is the result of both the positive and negative portions of the solution.