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

Multiply the exponents in ((j2-4002)12)2.

Apply the power rule and multiply exponents, (am)n=amn.

(j2-4002)12⋅2=152

Cancel the common factor of 2.

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.

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

Move all terms not containing j to the right side of the equation.

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.

Simplify the right side of the equation.

Rewrite 160225 as 52⋅6409.

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.

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