z^2+0.6z-20.16=0

Solution for z^2+0.6z-20.16=0 equation:

Simplifying
z2 + 0.6z + -20.16 = 0

Reorder the terms:
-20.16 + 0.6z + z2 = 0

Solving
-20.16 + 0.6z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '20.16' to each side of the equation.
-20.16 + 0.6z + 20.16 + z2 = 0 + 20.16

Reorder the terms:
-20.16 + 20.16 + 0.6z + z2 = 0 + 20.16

Combine like terms: -20.16 + 20.16 = 0.00
0.00 + 0.6z + z2 = 0 + 20.16
0.6z + z2 = 0 + 20.16

Combine like terms: 0 + 20.16 = 20.16
0.6z + z2 = 20.16

The z term is 0.6z.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6z + 0.09 + z2 = 20.16 + 0.09

Reorder the terms:
0.09 + 0.6z + z2 = 20.16 + 0.09

Combine like terms: 20.16 + 0.09 = 20.25
0.09 + 0.6z + z2 = 20.25

Factor a perfect square on the left side:
(z + 0.3)(z + 0.3) = 20.25

Calculate the square root of the right side: 4.5

Break this problem into two subproblems by setting 
(z + 0.3) equal to 4.5 and -4.5.

Subproblem 1
z + 0.3 = 4.5

Simplifying
z + 0.3 = 4.5

Reorder the terms:
0.3 + z = 4.5

Solving
0.3 + z = 4.5

Solving for variable 'z'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + z = 4.5 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + z = 4.5 + -0.3
z = 4.5 + -0.3

Combine like terms: 4.5 + -0.3 = 4.2
z = 4.2

Simplifying
z = 4.2

Subproblem 2
z + 0.3 = -4.5

Simplifying
z + 0.3 = -4.5

Reorder the terms:
0.3 + z = -4.5

Solving
0.3 + z = -4.5

Solving for variable 'z'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + z = -4.5 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + z = -4.5 + -0.3
z = -4.5 + -0.3

Combine like terms: -4.5 + -0.3 = -4.8
z = -4.8

Simplifying
z = -4.8

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {4.2, -4.8}