Basic Math Examples

Solve for z z=4 square root of z-4
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
Apply the product rule to .
Step 3.2.1.2
Raise to the power of .
Step 3.2.1.3
Multiply the exponents in .
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Step 3.2.1.3.1
Apply the power rule and multiply exponents, .
Step 3.2.1.3.2
Cancel the common factor of .
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Step 3.2.1.3.2.1
Cancel the common factor.
Step 3.2.1.3.2.2
Rewrite the expression.
Step 3.2.1.4
Simplify.
Step 3.2.1.5
Apply the distributive property.
Step 3.2.1.6
Multiply by .
Step 4
Solve for .
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Factor the left side of the equation.
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Step 4.2.1
Factor out of .
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Step 4.2.1.1
Reorder the expression.
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Step 4.2.1.1.1
Move .
Step 4.2.1.1.2
Reorder and .
Step 4.2.1.2
Factor out of .
Step 4.2.1.3
Factor out of .
Step 4.2.1.4
Rewrite as .
Step 4.2.1.5
Factor out of .
Step 4.2.1.6
Factor out of .
Step 4.2.2
Factor using the perfect square rule.
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Step 4.2.2.1
Rewrite as .
Step 4.2.2.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 4.2.2.3
Rewrite the polynomial.
Step 4.2.2.4
Factor using the perfect square trinomial rule , where and .
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
Dividing two negative values results in a positive value.
Step 4.3.2.2
Divide by .
Step 4.3.3
Simplify the right side.
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Step 4.3.3.1
Divide by .
Step 4.4
Set the equal to .
Step 4.5
Add to both sides of the equation.