Basic Math Examples

Solve for z square root of 3z+2 = square root of 8z-8
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
Simplify the left side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Multiply the exponents in .
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Step 2.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.2.1.1.2
Cancel the common factor of .
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Step 2.2.1.1.2.1
Cancel the common factor.
Step 2.2.1.1.2.2
Rewrite the expression.
Step 2.2.1.2
Simplify.
Step 2.3
Simplify the right side.
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Step 2.3.1
Simplify .
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Step 2.3.1.1
Factor out of .
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Step 2.3.1.1.1
Factor out of .
Step 2.3.1.1.2
Factor out of .
Step 2.3.1.1.3
Factor out of .
Step 2.3.1.2
Rewrite as .
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Step 2.3.1.2.1
Factor out of .
Step 2.3.1.2.2
Rewrite as .
Step 2.3.1.2.3
Add parentheses.
Step 2.3.1.3
Pull terms out from under the radical.
Step 2.3.1.4
Simplify the expression.
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Step 2.3.1.4.1
Apply the product rule to .
Step 2.3.1.4.2
Raise to the power of .
Step 2.3.1.5
Rewrite as .
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Step 2.3.1.5.1
Use to rewrite as .
Step 2.3.1.5.2
Apply the power rule and multiply exponents, .
Step 2.3.1.5.3
Combine and .
Step 2.3.1.5.4
Cancel the common factor of .
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Step 2.3.1.5.4.1
Cancel the common factor.
Step 2.3.1.5.4.2
Rewrite the expression.
Step 2.3.1.5.5
Simplify.
Step 2.3.1.6
Apply the distributive property.
Step 2.3.1.7
Multiply by .
Step 2.3.1.8
Apply the distributive property.
Step 2.3.1.9
Multiply.
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Step 2.3.1.9.1
Multiply by .
Step 2.3.1.9.2
Multiply by .
Step 3
Solve for .
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Step 3.1
Move all terms containing to the left side of the equation.
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Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
Subtract from .
Step 3.2
Move all terms not containing to the right side of the equation.
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Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Subtract from .
Step 3.3
Divide each term in by and simplify.
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Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
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Step 3.3.2.1
Cancel the common factor of .
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Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 3.3.3
Simplify the right side.
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Step 3.3.3.1
Divide by .