1.21z^2+5.28z+5.76=0

Solution for 1.21z^2+5.28z+5.76=0 equation:

Simplifying
1.21z2 + 5.28z + 5.76 = 0

Reorder the terms:
5.76 + 5.28z + 1.21z2 = 0

Solving
5.76 + 5.28z + 1.21z2 = 0

Solving for variable 'z'.

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

Divide each side by '1.21'.
4.760330579 + 4.363636364z + z2 = 0

Move the constant term to the right:

Add '-4.760330579' to each side of the equation.
4.760330579 + 4.363636364z + -4.760330579 + z2 = 0 + -4.760330579

Reorder the terms:
4.760330579 + -4.760330579 + 4.363636364z + z2 = 0 + -4.760330579

Combine like terms: 4.760330579 + -4.760330579 = 0.000000000
0.000000000 + 4.363636364z + z2 = 0 + -4.760330579
4.363636364z + z2 = 0 + -4.760330579

Combine like terms: 0 + -4.760330579 = -4.760330579
4.363636364z + z2 = -4.760330579

The z term is 4.363636364z.  Take half its coefficient (2.181818182).
Square it (4.760330579) and add it to both sides.

Add '4.760330579' to each side of the equation.
4.363636364z + 4.760330579 + z2 = -4.760330579 + 4.760330579

Reorder the terms:
4.760330579 + 4.363636364z + z2 = -4.760330579 + 4.760330579

Combine like terms: -4.760330579 + 4.760330579 = 0.000000000
4.760330579 + 4.363636364z + z2 = 0.000000000

Factor a perfect square on the left side:
(z + 2.181818182)(z + 2.181818182) = 0.000000000

Calculate the square root of the right side: 0.000000000

Break this problem into two subproblems by setting 
(z + 2.181818182) equal to 0.000000000 and 0.000000000.

Subproblem 1
z + 2.181818182 = 0.000000000

Simplifying
z + 2.181818182 = 0.000000000

Reorder the terms:
2.181818182 + z = 0.000000000

Solving
2.181818182 + z = 0.000000000

Solving for variable 'z'.

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

Add '-2.181818182' to each side of the equation.
2.181818182 + -2.181818182 + z = 0.000000000 + -2.181818182

Combine like terms: 2.181818182 + -2.181818182 = 0.000000000
0.000000000 + z = 0.000000000 + -2.181818182
z = 0.000000000 + -2.181818182

Combine like terms: 0.000000000 + -2.181818182 = -2.181818182
z = -2.181818182

Simplifying
z = -2.181818182

Subproblem 2
z + 2.181818182 = 0.000000000

Simplifying
z + 2.181818182 = 0.000000000

Reorder the terms:
2.181818182 + z = 0.000000000

Solving
2.181818182 + z = 0.000000000

Solving for variable 'z'.

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

Add '-2.181818182' to each side of the equation.
2.181818182 + -2.181818182 + z = 0.000000000 + -2.181818182

Combine like terms: 2.181818182 + -2.181818182 = 0.000000000
0.000000000 + z = 0.000000000 + -2.181818182
z = 0.000000000 + -2.181818182

Combine like terms: 0.000000000 + -2.181818182 = -2.181818182
z = -2.181818182

Simplifying
z = -2.181818182

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-2.181818182, -2.181818182}