64z^2-1616z+1=0

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Solution for 64z^2-1616z+1=0 equation: 


Simplifying
64z2 + -1616z + 1 = 0

Reorder the terms:
1 + -1616z + 64z2 = 0

Solving
1 + -1616z + 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 + -25.25z + z2 = 0

Move the constant term to the right:

Add '-0.015625' to each side of the equation.
0.015625 + -25.25z + -0.015625 + z2 = 0 + -0.015625

Reorder the terms:
0.015625 + -0.015625 + -25.25z + z2 = 0 + -0.015625

Combine like terms: 0.015625 + -0.015625 = 0.000000
0.000000 + -25.25z + z2 = 0 + -0.015625
-25.25z + z2 = 0 + -0.015625

Combine like terms: 0 + -0.015625 = -0.015625
-25.25z + z2 = -0.015625

The z term is -25.25z.  Take half its coefficient (-12.625).
Square it (159.390625) and add it to both sides.

Add '159.390625' to each side of the equation.
-25.25z + 159.390625 + z2 = -0.015625 + 159.390625

Reorder the terms:
159.390625 + -25.25z + z2 = -0.015625 + 159.390625

Combine like terms: -0.015625 + 159.390625 = 159.375
159.390625 + -25.25z + z2 = 159.375

Factor a perfect square on the left side:
(z + -12.625)(z + -12.625) = 159.375

Calculate the square root of the right side: 12.624381173

Break this problem into two subproblems by setting 
(z + -12.625) equal to 12.624381173 and -12.624381173.


Subproblem 1
z + -12.625 = 12.624381173

Simplifying
z + -12.625 = 12.624381173

Reorder the terms:
-12.625 + z = 12.624381173

Solving
-12.625 + z = 12.624381173

Solving for variable 'z'.

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

Add '12.625' to each side of the equation.
-12.625 + 12.625 + z = 12.624381173 + 12.625

Combine like terms: -12.625 + 12.625 = 0.000
0.000 + z = 12.624381173 + 12.625
z = 12.624381173 + 12.625

Combine like terms: 12.624381173 + 12.625 = 25.249381173
z = 25.249381173

Simplifying
z = 25.249381173


Subproblem 2
z + -12.625 = -12.624381173

Simplifying
z + -12.625 = -12.624381173

Reorder the terms:
-12.625 + z = -12.624381173

Solving
-12.625 + z = -12.624381173

Solving for variable 'z'.

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

Add '12.625' to each side of the equation.
-12.625 + 12.625 + z = -12.624381173 + 12.625

Combine like terms: -12.625 + 12.625 = 0.000
0.000 + z = -12.624381173 + 12.625
z = -12.624381173 + 12.625

Combine like terms: -12.624381173 + 12.625 = 0.000618827
z = 0.000618827

Simplifying
z = 0.000618827


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {25.249381173, 0.000618827}

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