(4+2*j)-(-4-2*j)-(7-j)+j*(5-4*j)=

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Solution for (4+2*j)-(-4-2*j)-(7-j)+j*(5-4*j)= equation:


Simplifying
(4 + 2j) + -1(-4 + -2j) + -1(7 + -1j) + j(5 + -4j) = 0

Remove parenthesis around (4 + 2j)
4 + 2j + -1(-4 + -2j) + -1(7 + -1j) + j(5 + -4j) = 0
4 + 2j + (-4 * -1 + -2j * -1) + -1(7 + -1j) + j(5 + -4j) = 0
4 + 2j + (4 + 2j) + -1(7 + -1j) + j(5 + -4j) = 0
4 + 2j + 4 + 2j + (7 * -1 + -1j * -1) + j(5 + -4j) = 0
4 + 2j + 4 + 2j + (-7 + 1j) + j(5 + -4j) = 0
4 + 2j + 4 + 2j + -7 + 1j + (5 * j + -4j * j) = 0
4 + 2j + 4 + 2j + -7 + 1j + (5j + -4j2) = 0

Reorder the terms:
4 + 4 + -7 + 2j + 2j + 1j + 5j + -4j2 = 0

Combine like terms: 4 + 4 = 8
8 + -7 + 2j + 2j + 1j + 5j + -4j2 = 0

Combine like terms: 8 + -7 = 1
1 + 2j + 2j + 1j + 5j + -4j2 = 0

Combine like terms: 2j + 2j = 4j
1 + 4j + 1j + 5j + -4j2 = 0

Combine like terms: 4j + 1j = 5j
1 + 5j + 5j + -4j2 = 0

Combine like terms: 5j + 5j = 10j
1 + 10j + -4j2 = 0

Solving
1 + 10j + -4j2 = 0

Solving for variable 'j'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + -2.5j + j2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -2.5j + 0.25 + j2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -2.5j + j2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -2.5j + j2 = 0 + 0.25
-2.5j + j2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-2.5j + j2 = 0.25

The j term is -2.5j.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5j + 1.5625 + j2 = 0.25 + 1.5625

Reorder the terms:
1.5625 + -2.5j + j2 = 0.25 + 1.5625

Combine like terms: 0.25 + 1.5625 = 1.8125
1.5625 + -2.5j + j2 = 1.8125

Factor a perfect square on the left side:
(j + -1.25)(j + -1.25) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(j + -1.25) equal to 1.346291202 and -1.346291202.

Subproblem 1

j + -1.25 = 1.346291202 Simplifying j + -1.25 = 1.346291202 Reorder the terms: -1.25 + j = 1.346291202 Solving -1.25 + j = 1.346291202 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + j = 1.346291202 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + j = 1.346291202 + 1.25 j = 1.346291202 + 1.25 Combine like terms: 1.346291202 + 1.25 = 2.596291202 j = 2.596291202 Simplifying j = 2.596291202

Subproblem 2

j + -1.25 = -1.346291202 Simplifying j + -1.25 = -1.346291202 Reorder the terms: -1.25 + j = -1.346291202 Solving -1.25 + j = -1.346291202 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + j = -1.346291202 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + j = -1.346291202 + 1.25 j = -1.346291202 + 1.25 Combine like terms: -1.346291202 + 1.25 = -0.096291202 j = -0.096291202 Simplifying j = -0.096291202

Solution

The solution to the problem is based on the solutions from the subproblems. j = {2.596291202, -0.096291202}

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