49z^2-28z-4=0

Solution for 49z^2-28z-4=0 equation:

Simplifying
49z2 + -28z + -4 = 0

Reorder the terms:
-4 + -28z + 49z2 = 0

Solving
-4 + -28z + 49z2 = 0

Solving for variable 'z'.

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

Divide each side by '49'.
-0.08163265306 + -0.5714285714z + z2 = 0

Move the constant term to the right:

Add '0.08163265306' to each side of the equation.
-0.08163265306 + -0.5714285714z + 0.08163265306 + z2 = 0 + 0.08163265306

Reorder the terms:
-0.08163265306 + 0.08163265306 + -0.5714285714z + z2 = 0 + 0.08163265306

Combine like terms: -0.08163265306 + 0.08163265306 = 0.00000000000
0.00000000000 + -0.5714285714z + z2 = 0 + 0.08163265306
-0.5714285714z + z2 = 0 + 0.08163265306

Combine like terms: 0 + 0.08163265306 = 0.08163265306
-0.5714285714z + z2 = 0.08163265306

The z term is -0.5714285714z.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714z + 0.08163265305 + z2 = 0.08163265306 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714z + z2 = 0.08163265306 + 0.08163265305

Combine like terms: 0.08163265306 + 0.08163265305 = 0.16326530611
0.08163265305 + -0.5714285714z + z2 = 0.16326530611

Factor a perfect square on the left side:
(z + -0.2857142857)(z + -0.2857142857) = 0.16326530611

Calculate the square root of the right side: 0.404061018

Break this problem into two subproblems by setting 
(z + -0.2857142857) equal to 0.404061018 and -0.404061018.

Subproblem 1
z + -0.2857142857 = 0.404061018

Simplifying
z + -0.2857142857 = 0.404061018

Reorder the terms:
-0.2857142857 + z = 0.404061018

Solving
-0.2857142857 + z = 0.404061018

Solving for variable 'z'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + z = 0.404061018 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + z = 0.404061018 + 0.2857142857
z = 0.404061018 + 0.2857142857

Combine like terms: 0.404061018 + 0.2857142857 = 0.6897753037
z = 0.6897753037

Simplifying
z = 0.6897753037

Subproblem 2
z + -0.2857142857 = -0.404061018

Simplifying
z + -0.2857142857 = -0.404061018

Reorder the terms:
-0.2857142857 + z = -0.404061018

Solving
-0.2857142857 + z = -0.404061018

Solving for variable 'z'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + z = -0.404061018 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + z = -0.404061018 + 0.2857142857
z = -0.404061018 + 0.2857142857

Combine like terms: -0.404061018 + 0.2857142857 = -0.1183467323
z = -0.1183467323

Simplifying
z = -0.1183467323

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.6897753037, -0.1183467323}