Basic Math Examples

Solve for j 15 = square root of j^2-400^2
Step 1
Rewrite the equation as .
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
Multiply the exponents in .
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Step 3.2.1.1.1
Apply the power rule and multiply exponents, .
Step 3.2.1.1.2
Cancel the common factor of .
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Step 3.2.1.1.2.1
Cancel the common factor.
Step 3.2.1.1.2.2
Rewrite the expression.
Step 3.2.1.2
Simplify each term.
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Step 3.2.1.2.1
Raise to the power of .
Step 3.2.1.2.2
Multiply by .
Step 3.2.1.3
Simplify.
Step 3.3
Simplify the right side.
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Step 3.3.1
Raise to the power of .
Step 4
Solve for .
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Step 4.1
Move all terms not containing to the right side of the equation.
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Step 4.1.1
Add to both sides of the equation.
Step 4.1.2
Add and .
Step 4.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 4.3
Simplify .
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Step 4.3.1
Rewrite as .
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Step 4.3.1.1
Factor out of .
Step 4.3.1.2
Rewrite as .
Step 4.3.2
Pull terms out from under the radical.
Step 4.4
The complete solution is the result of both the positive and negative portions of the solution.
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Step 4.4.1
First, use the positive value of the to find the first solution.
Step 4.4.2
Next, use the negative value of the to find the second solution.
Step 4.4.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: