j^2+15j-4=0

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Solution for j^2+15j-4=0 equation:


Simplifying
j2 + 15j + -4 = 0

Reorder the terms:
-4 + 15j + j2 = 0

Solving
-4 + 15j + j2 = 0

Solving for variable 'j'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 15j + 4 + j2 = 0 + 4

Reorder the terms:
-4 + 4 + 15j + j2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 15j + j2 = 0 + 4
15j + j2 = 0 + 4

Combine like terms: 0 + 4 = 4
15j + j2 = 4

The j term is 15j.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15j + 56.25 + j2 = 4 + 56.25

Reorder the terms:
56.25 + 15j + j2 = 4 + 56.25

Combine like terms: 4 + 56.25 = 60.25
56.25 + 15j + j2 = 60.25

Factor a perfect square on the left side:
(j + 7.5)(j + 7.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(j + 7.5) equal to 7.762087348 and -7.762087348.

Subproblem 1

j + 7.5 = 7.762087348 Simplifying j + 7.5 = 7.762087348 Reorder the terms: 7.5 + j = 7.762087348 Solving 7.5 + j = 7.762087348 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + j = 7.762087348 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + j = 7.762087348 + -7.5 j = 7.762087348 + -7.5 Combine like terms: 7.762087348 + -7.5 = 0.262087348 j = 0.262087348 Simplifying j = 0.262087348

Subproblem 2

j + 7.5 = -7.762087348 Simplifying j + 7.5 = -7.762087348 Reorder the terms: 7.5 + j = -7.762087348 Solving 7.5 + j = -7.762087348 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + j = -7.762087348 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + j = -7.762087348 + -7.5 j = -7.762087348 + -7.5 Combine like terms: -7.762087348 + -7.5 = -15.262087348 j = -15.262087348 Simplifying j = -15.262087348

Solution

The solution to the problem is based on the solutions from the subproblems. j = {0.262087348, -15.262087348}

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