64z^2-1212z+1=0

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Solution for 64z^2-1212z+1=0 equation: 


Simplifying
64z2 + -1212z + 1 = 0

Reorder the terms:
1 + -1212z + 64z2 = 0

Solving
1 + -1212z + 64z2 = 0

Solving for variable 'z'.

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

Divide each side by '64'.
0.015625 + -18.9375z + z2 = 0

Move the constant term to the right:

Add '-0.015625' to each side of the equation.
0.015625 + -18.9375z + -0.015625 + z2 = 0 + -0.015625

Reorder the terms:
0.015625 + -0.015625 + -18.9375z + z2 = 0 + -0.015625

Combine like terms: 0.015625 + -0.015625 = 0.000000
0.000000 + -18.9375z + z2 = 0 + -0.015625
-18.9375z + z2 = 0 + -0.015625

Combine like terms: 0 + -0.015625 = -0.015625
-18.9375z + z2 = -0.015625

The z term is -18.9375z.  Take half its coefficient (-9.46875).
Square it (89.65722656) and add it to both sides.

Add '89.65722656' to each side of the equation.
-18.9375z + 89.65722656 + z2 = -0.015625 + 89.65722656

Reorder the terms:
89.65722656 + -18.9375z + z2 = -0.015625 + 89.65722656

Combine like terms: -0.015625 + 89.65722656 = 89.64160156
89.65722656 + -18.9375z + z2 = 89.64160156

Factor a perfect square on the left side:
(z + -9.46875)(z + -9.46875) = 89.64160156

Calculate the square root of the right side: 9.467924881

Break this problem into two subproblems by setting 
(z + -9.46875) equal to 9.467924881 and -9.467924881.


Subproblem 1
z + -9.46875 = 9.467924881

Simplifying
z + -9.46875 = 9.467924881

Reorder the terms:
-9.46875 + z = 9.467924881

Solving
-9.46875 + z = 9.467924881

Solving for variable 'z'.

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

Add '9.46875' to each side of the equation.
-9.46875 + 9.46875 + z = 9.467924881 + 9.46875

Combine like terms: -9.46875 + 9.46875 = 0.00000
0.00000 + z = 9.467924881 + 9.46875
z = 9.467924881 + 9.46875

Combine like terms: 9.467924881 + 9.46875 = 18.936674881
z = 18.936674881

Simplifying
z = 18.936674881


Subproblem 2
z + -9.46875 = -9.467924881

Simplifying
z + -9.46875 = -9.467924881

Reorder the terms:
-9.46875 + z = -9.467924881

Solving
-9.46875 + z = -9.467924881

Solving for variable 'z'.

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

Add '9.46875' to each side of the equation.
-9.46875 + 9.46875 + z = -9.467924881 + 9.46875

Combine like terms: -9.46875 + 9.46875 = 0.00000
0.00000 + z = -9.467924881 + 9.46875
z = -9.467924881 + 9.46875

Combine like terms: -9.467924881 + 9.46875 = 0.000825119
z = 0.000825119

Simplifying
z = 0.000825119


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {18.936674881, 0.000825119}

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