Basic Math Examples

Solve for s 5s(4-s)^(-1/2)-6 square root of 4-s=0
Step 1
Solve for .
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Step 1.1
Simplify each term.
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Step 1.1.1
Rewrite the expression using the negative exponent rule .
Step 1.1.2
Multiply .
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Step 1.1.2.1
Combine and .
Step 1.1.2.2
Combine and .
Step 1.1.3
Move to the left of .
Step 1.2
Subtract from both sides 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.
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Step 3.2.1.6.1
Multiply by .
Step 3.2.1.6.2
Multiply by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Simplify .
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Step 3.3.1.1
Use the power rule to distribute the exponent.
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Step 3.3.1.1.1
Apply the product rule to .
Step 3.3.1.1.2
Apply the product rule to .
Step 3.3.1.1.3
Apply the product rule to .
Step 3.3.1.2
Simplify the expression.
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Step 3.3.1.2.1
Raise to the power of .
Step 3.3.1.2.2
Multiply by .
Step 3.3.1.2.3
Raise to the power of .
Step 3.3.1.3
Simplify the denominator.
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Step 3.3.1.3.1
Multiply the exponents in .
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Step 3.3.1.3.1.1
Apply the power rule and multiply exponents, .
Step 3.3.1.3.1.2
Cancel the common factor of .
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Step 3.3.1.3.1.2.1
Cancel the common factor.
Step 3.3.1.3.1.2.2
Rewrite the expression.
Step 3.3.1.3.2
Simplify.
Step 4
Solve for .
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Find the LCD of the terms in the equation.
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Step 4.2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 4.2.2
Remove parentheses.
Step 4.2.3
The LCM of one and any expression is the expression.
Step 4.3
Multiply each term in by to eliminate the fractions.
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Step 4.3.1
Multiply each term in by .
Step 4.3.2
Simplify the left side.
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Step 4.3.2.1
Simplify by multiplying through.
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Step 4.3.2.1.1
Apply the distributive property.
Step 4.3.2.1.2
Simplify the expression.
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Step 4.3.2.1.2.1
Multiply by .
Step 4.3.2.1.2.2
Rewrite using the commutative property of multiplication.
Step 4.3.2.2
Simplify each term.
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Step 4.3.2.2.1
Multiply by by adding the exponents.
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Step 4.3.2.2.1.1
Move .
Step 4.3.2.2.1.2
Multiply by .
Step 4.3.2.2.2
Multiply by .
Step 4.3.3
Simplify the right side.
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Step 4.3.3.1
Simplify each term.
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Step 4.3.3.1.1
Cancel the common factor of .
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Step 4.3.3.1.1.1
Cancel the common factor.
Step 4.3.3.1.1.2
Rewrite the expression.
Step 4.3.3.1.2
Apply the distributive property.
Step 4.3.3.1.3
Multiply by .
Step 4.3.3.1.4
Multiply by .
Step 4.4
Solve the equation.
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Step 4.4.1
Move all terms containing to the left side of the equation.
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Step 4.4.1.1
Subtract from both sides of the equation.
Step 4.4.1.2
Subtract from both sides of the equation.
Step 4.4.1.3
Subtract from .
Step 4.4.1.4
Subtract from .
Step 4.4.2
Add to both sides of the equation.
Step 4.4.3
Factor by grouping.
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Step 4.4.3.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 4.4.3.1.1
Factor out of .
Step 4.4.3.1.2
Rewrite as plus
Step 4.4.3.1.3
Apply the distributive property.
Step 4.4.3.2
Factor out the greatest common factor from each group.
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Step 4.4.3.2.1
Group the first two terms and the last two terms.
Step 4.4.3.2.2
Factor out the greatest common factor (GCF) from each group.
Step 4.4.3.3
Factor the polynomial by factoring out the greatest common factor, .
Step 4.4.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.4.5
Set equal to and solve for .
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Step 4.4.5.1
Set equal to .
Step 4.4.5.2
Solve for .
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Step 4.4.5.2.1
Add to both sides of the equation.
Step 4.4.5.2.2
Divide each term in by and simplify.
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Step 4.4.5.2.2.1
Divide each term in by .
Step 4.4.5.2.2.2
Simplify the left side.
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Step 4.4.5.2.2.2.1
Cancel the common factor of .
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Step 4.4.5.2.2.2.1.1
Cancel the common factor.
Step 4.4.5.2.2.2.1.2
Divide by .
Step 4.4.6
Set equal to and solve for .
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Step 4.4.6.1
Set equal to .
Step 4.4.6.2
Add to both sides of the equation.
Step 4.4.7
The final solution is all the values that make true.
Step 5
Exclude the solutions that do not make true.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: