z*z+16z+41=0

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Solution for z*z+16z+41=0 equation:


Simplifying
z * z + 16z + 41 = 0
Multiply z * z
z2 + 16z + 41 = 0
Reorder the terms:
41 + 16z + z2 = 0
Solving
41 + 16z + z2 = 0
Solving for variable 'z'.
Begin completing the square.
Move the constant term to the right:
Add '-41' to each side of the equation.
41 + 16z + -41 + z2 = 0 + -41
Reorder the terms:
41 + -41 + 16z + z2 = 0 + -41
Combine like terms: 41 + -41 = 0
0 + 16z + z2 = 0 + -41
16z + z2 = 0 + -41
Combine like terms: 0 + -41 = -41
16z + z2 = -41
The z term is 16z. Take half its coefficient (8).
Square it (64) and add it to both sides.
Add '64' to each side of the equation.
16z + 64 + z2 = -41 + 64
Reorder the terms:
64 + 16z + z2 = -41 + 64
Combine like terms: -41 + 64 = 23
64 + 16z + z2 = 23
Factor a perfect square on the left side:
(z + 8)(z + 8) = 23
Calculate the square root of the right side: 4.795831523
Break this problem into two subproblems by setting 
(z + 8) equal to 4.795831523 and -4.795831523.

Subproblem 1

z + 8 = 4.795831523 Simplifying z + 8 = 4.795831523 Reorder the terms: 8 + z = 4.795831523 Solving 8 + z = 4.795831523 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z = 4.795831523 + -8 Combine like terms: 8 + -8 = 0 0 + z = 4.795831523 + -8 z = 4.795831523 + -8 Combine like terms: 4.795831523 + -8 = -3.204168477 z = -3.204168477 Simplifying z = -3.204168477

Subproblem 2

z + 8 = -4.795831523 Simplifying z + 8 = -4.795831523 Reorder the terms: 8 + z = -4.795831523 Solving 8 + z = -4.795831523 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z = -4.795831523 + -8 Combine like terms: 8 + -8 = 0 0 + z = -4.795831523 + -8 z = -4.795831523 + -8 Combine like terms: -4.795831523 + -8 = -12.795831523 z = -12.795831523 Simplifying z = -12.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-3.204168477, -12.795831523}

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