Basic Math Examples

Solve for y fourth root of 4y^2-3=-y
Step 1
To remove the radical on the left side of the equation, raise both sides of the equation to the power of .
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
Apply the product rule to .
Step 2.3.1.2
Raise to the power of .
Step 2.3.1.3
Multiply by .
Step 3
Solve for .
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Step 3.1
Subtract from both sides of the equation.
Step 3.2
Substitute into the equation. This will make the quadratic formula easy to use.
Step 3.3
Factor the left side of the equation.
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Step 3.3.1
Factor out of .
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Step 3.3.1.1
Factor out of .
Step 3.3.1.2
Factor out of .
Step 3.3.1.3
Rewrite as .
Step 3.3.1.4
Factor out of .
Step 3.3.1.5
Factor out of .
Step 3.3.2
Factor.
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Step 3.3.2.1
Factor using the AC method.
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Step 3.3.2.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 3.3.2.1.2
Write the factored form using these integers.
Step 3.3.2.2
Remove unnecessary parentheses.
Step 3.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.5
Set equal to and solve for .
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Step 3.5.1
Set equal to .
Step 3.5.2
Add to both sides of the equation.
Step 3.6
Set equal to and solve for .
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Step 3.6.1
Set equal to .
Step 3.6.2
Add to both sides of the equation.
Step 3.7
The final solution is all the values that make true.
Step 3.8
Substitute the real value of back into the solved equation.
Step 3.9
Solve the first equation for .
Step 3.10
Solve the equation for .
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Step 3.10.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.10.2
The complete solution is the result of both the positive and negative portions of the solution.
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Step 3.10.2.1
First, use the positive value of the to find the first solution.
Step 3.10.2.2
Next, use the negative value of the to find the second solution.
Step 3.10.2.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 3.11
Solve the second equation for .
Step 3.12
Solve the equation for .
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Step 3.12.1
Remove parentheses.
Step 3.12.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.12.3
Any root of is .
Step 3.12.4
The complete solution is the result of both the positive and negative portions of the solution.
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Step 3.12.4.1
First, use the positive value of the to find the first solution.
Step 3.12.4.2
Next, use the negative value of the to find the second solution.
Step 3.12.4.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 3.13
The solution to is .
Step 4
Exclude the solutions that do not make true.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: