4j^2+104j-100=0

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Solution for 4j^2+104j-100=0 equation: 


Simplifying
4j2 + 104j + -100 = 0

Reorder the terms:
-100 + 104j + 4j2 = 0

Solving
-100 + 104j + 4j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + 26j + j2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-25 + 26j + j2)' equal to zero and attempt to solve:

Simplifying
-25 + 26j + j2 = 0

Solving
-25 + 26j + j2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 26j + 25 + j2 = 0 + 25

Reorder the terms:
-25 + 25 + 26j + j2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 26j + j2 = 0 + 25
26j + j2 = 0 + 25

Combine like terms: 0 + 25 = 25
26j + j2 = 25

The j term is 26j.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26j + 169 + j2 = 25 + 169

Reorder the terms:
169 + 26j + j2 = 25 + 169

Combine like terms: 25 + 169 = 194
169 + 26j + j2 = 194

Factor a perfect square on the left side:
(j + 13)(j + 13) = 194

Calculate the square root of the right side: 13.928388277

Break this problem into two subproblems by setting 
(j + 13) equal to 13.928388277 and -13.928388277.


Subproblem 1
j + 13 = 13.928388277

Simplifying
j + 13 = 13.928388277

Reorder the terms:
13 + j = 13.928388277

Solving
13 + j = 13.928388277

Solving for variable 'j'.

Move all terms containing j to the left, all other terms to the right.

Add '-13' to each side of the equation.
13 + -13 + j = 13.928388277 + -13

Combine like terms: 13 + -13 = 0
0 + j = 13.928388277 + -13
j = 13.928388277 + -13

Combine like terms: 13.928388277 + -13 = 0.928388277
j = 0.928388277

Simplifying
j = 0.928388277


Subproblem 2
j + 13 = -13.928388277

Simplifying
j + 13 = -13.928388277

Reorder the terms:
13 + j = -13.928388277

Solving
13 + j = -13.928388277

Solving for variable 'j'.

Move all terms containing j to the left, all other terms to the right.

Add '-13' to each side of the equation.
13 + -13 + j = -13.928388277 + -13

Combine like terms: 13 + -13 = 0
0 + j = -13.928388277 + -13
j = -13.928388277 + -13

Combine like terms: -13.928388277 + -13 = -26.928388277
j = -26.928388277

Simplifying
j = -26.928388277


Solution
The solution to the problem is based on the solutions
from the subproblems.
j = {0.928388277, -26.928388277}
Solution
j = {0.928388277, -26.928388277}

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