Solve for j 15 = square root of j^2-400^2

Math
15=j2-4002
Rewrite the equation as j2-4002=15.
j2-4002=15
To remove the radical on the left side of the equation, square both sides of the equation.
j2-40022=152
Simplify each side of the equation.
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Multiply the exponents in ((j2-4002)12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(j2-4002)12⋅2=152
Cancel the common factor of 2.
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Cancel the common factor.
(j2-4002)12⋅2=152
Rewrite the expression.
(j2-4002)1=152
(j2-4002)1=152
(j2-4002)1=152
Simplify each term.
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Raise 400 to the power of 2.
(j2-1⋅160000)1=152
Multiply -1 by 160000.
(j2-160000)1=152
(j2-160000)1=152
Simplify.
j2-160000=152
Raise 15 to the power of 2.
j2-160000=225
j2-160000=225
Solve for j.
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Move all terms not containing j to the right side of the equation.
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Add 160000 to both sides of the equation.
j2=225+160000
Add 225 and 160000.
j2=160225
j2=160225
Take the square root of both sides of the equation to eliminate the exponent on the left side.
j=±160225
The complete solution is the result of both the positive and negative portions of the solution.
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Simplify the right side of the equation.
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Rewrite 160225 as 52⋅6409.
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Factor 25 out of 160225.
j=±25(6409)
Rewrite 25 as 52.
j=±52⋅6409
j=±52⋅6409
Pull terms out from under the radical.
j=±56409
j=±56409
The complete solution is the result of both the positive and negative portions of the solution.
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First, use the positive value of the ± to find the first solution.
j=56409
Next, use the negative value of the ± to find the second solution.
j=-56409
The complete solution is the result of both the positive and negative portions of the solution.
j=56409,-56409
j=56409,-56409
j=56409,-56409
j=56409,-56409
The result can be shown in multiple forms.
Exact Form:
j=56409,-56409
Decimal Form:
j=400.28115119…,-400.28115119…
Solve for j 15 = square root of j^2-400^2

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