Algebra Examples

Solve for z square root of (z+5)^2=6
Step 1
To remove the radical on the left side of the equation, square both sides of the equation.
Step 2
Simplify each side of the equation.
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Step 2.1
Use to rewrite as .
Step 2.2
Divide by .
Step 2.3
Simplify the left side.
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Step 2.3.1
Multiply the exponents in .
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Step 2.3.1.1
Apply the power rule and multiply exponents, .
Step 2.3.1.2
Multiply by .
Step 2.4
Simplify the right side.
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Step 2.4.1
Raise to the power of .
Step 3
Solve for .
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Step 3.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.2
Simplify .
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Step 3.2.1
Rewrite as .
Step 3.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 3.3.1
First, use the positive value of the to find the first solution.
Step 3.3.2
Move all terms not containing to the right side of the equation.
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Step 3.3.2.1
Subtract from both sides of the equation.
Step 3.3.2.2
Subtract from .
Step 3.3.3
Next, use the negative value of the to find the second solution.
Step 3.3.4
Move all terms not containing to the right side of the equation.
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Step 3.3.4.1
Subtract from both sides of the equation.
Step 3.3.4.2
Subtract from .
Step 3.3.5
The complete solution is the result of both the positive and negative portions of the solution.