Simplifying
j^{2} + -3.5j + 1.5 = 0
Reorder the terms:
1.5 + -3.5j + j^{2} = 0
Solving
1.5 + -3.5j + j^{2} = 0
Solving for variable 'j'.
Begin completing the square.
Move the constant term to the right:
Add '-1.5' to each side of the equation.
1.5 + -3.5j + -1.5 + j^{2} = 0 + -1.5
Reorder the terms:
1.5 + -1.5 + -3.5j + j^{2} = 0 + -1.5
Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -3.5j + j^{2} = 0 + -1.5
-3.5j + j^{2} = 0 + -1.5
Combine like terms: 0 + -1.5 = -1.5
-3.5j + j^{2} = -1.5
The j term is -3.5j. Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.
Add '3.0625' to each side of the equation.
-3.5j + 3.0625 + j^{2} = -1.5 + 3.0625
Reorder the terms:
3.0625 + -3.5j + j^{2} = -1.5 + 3.0625
Combine like terms: -1.5 + 3.0625 = 1.5625
3.0625 + -3.5j + j^{2} = 1.5625
Factor a perfect square on the left side:
(j + -1.75)(j + -1.75) = 1.5625
Calculate the square root of the right side: 1.25
Break this problem into two subproblems by setting
(j + -1.75) equal to 1.25 and -1.25.
#### Subproblem 1

j + -1.75 = 1.25
Simplifying
j + -1.75 = 1.25
Reorder the terms:
-1.75 + j = 1.25
Solving
-1.75 + j = 1.25
Solving for variable 'j'.
Move all terms containing j to the left, all other terms to the right.
Add '1.75' to each side of the equation.
-1.75 + 1.75 + j = 1.25 + 1.75
Combine like terms: -1.75 + 1.75 = 0.00
0.00 + j = 1.25 + 1.75
j = 1.25 + 1.75
Combine like terms: 1.25 + 1.75 = 3
j = 3
Simplifying
j = 3
#### Subproblem 2

j + -1.75 = -1.25
Simplifying
j + -1.75 = -1.25
Reorder the terms:
-1.75 + j = -1.25
Solving
-1.75 + j = -1.25
Solving for variable 'j'.
Move all terms containing j to the left, all other terms to the right.
Add '1.75' to each side of the equation.
-1.75 + 1.75 + j = -1.25 + 1.75
Combine like terms: -1.75 + 1.75 = 0.00
0.00 + j = -1.25 + 1.75
j = -1.25 + 1.75
Combine like terms: -1.25 + 1.75 = 0.5
j = 0.5
Simplifying
j = 0.5
#### Solution

The solution to the problem is based on the solutions
from the subproblems.
j = {3, 0.5}