Basic Math Examples

Solve for a a = square root of 11^2-6a^2
Step 1
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 2
To remove the radical on the left side of the equation, square both sides of the equation.
Step 3
Simplify each side of the equation.
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Step 3.1
Use to rewrite as .
Step 3.2
Simplify the left side.
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Step 3.2.1
Simplify .
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Step 3.2.1.1
Multiply the exponents in .
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Step 3.2.1.1.1
Apply the power rule and multiply exponents, .
Step 3.2.1.1.2
Cancel the common factor of .
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Step 3.2.1.1.2.1
Cancel the common factor.
Step 3.2.1.1.2.2
Rewrite the expression.
Step 3.2.1.2
Raise to the power of .
Step 3.2.1.3
Simplify.
Step 4
Solve for .
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Step 4.1
Move all terms containing to the left side of the equation.
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Step 4.1.1
Subtract from both sides of the equation.
Step 4.1.2
Subtract from .
Step 4.2
Subtract from both sides of the equation.
Step 4.3
Divide each term in by and simplify.
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Step 4.3.1
Divide each term in by .
Step 4.3.2
Simplify the left side.
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Step 4.3.2.1
Cancel the common factor of .
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Step 4.3.2.1.1
Cancel the common factor.
Step 4.3.2.1.2
Divide by .
Step 4.3.3
Simplify the right side.
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Step 4.3.3.1
Dividing two negative values results in a positive value.
Step 4.4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 4.5
Simplify .
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Step 4.5.1
Rewrite as .
Step 4.5.2
Simplify the numerator.
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Step 4.5.2.1
Rewrite as .
Step 4.5.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 4.5.3
Multiply by .
Step 4.5.4
Combine and simplify the denominator.
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Step 4.5.4.1
Multiply by .
Step 4.5.4.2
Raise to the power of .
Step 4.5.4.3
Raise to the power of .
Step 4.5.4.4
Use the power rule to combine exponents.
Step 4.5.4.5
Add and .
Step 4.5.4.6
Rewrite as .
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Step 4.5.4.6.1
Use to rewrite as .
Step 4.5.4.6.2
Apply the power rule and multiply exponents, .
Step 4.5.4.6.3
Combine and .
Step 4.5.4.6.4
Cancel the common factor of .
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Step 4.5.4.6.4.1
Cancel the common factor.
Step 4.5.4.6.4.2
Rewrite the expression.
Step 4.5.4.6.5
Evaluate the exponent.
Step 4.6
The complete solution is the result of both the positive and negative portions of the solution.
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Step 4.6.1
First, use the positive value of the to find the first solution.
Step 4.6.2
Next, use the negative value of the to find the second solution.
Step 4.6.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 5
Exclude the solutions that do not make true.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: