64z^2-12144z+1=0

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Solution for 64z^2-12144z+1=0 equation: 


Simplifying
64z2 + -12144z + 1 = 0

Reorder the terms:
1 + -12144z + 64z2 = 0

Solving
1 + -12144z + 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 + -189.75z + z2 = 0

Move the constant term to the right:

Add '-0.015625' to each side of the equation.
0.015625 + -189.75z + -0.015625 + z2 = 0 + -0.015625

Reorder the terms:
0.015625 + -0.015625 + -189.75z + z2 = 0 + -0.015625

Combine like terms: 0.015625 + -0.015625 = 0.000000
0.000000 + -189.75z + z2 = 0 + -0.015625
-189.75z + z2 = 0 + -0.015625

Combine like terms: 0 + -0.015625 = -0.015625
-189.75z + z2 = -0.015625

The z term is -189.75z.  Take half its coefficient (-94.875).
Square it (9001.265625) and add it to both sides.

Add '9001.265625' to each side of the equation.
-189.75z + 9001.265625 + z2 = -0.015625 + 9001.265625

Reorder the terms:
9001.265625 + -189.75z + z2 = -0.015625 + 9001.265625

Combine like terms: -0.015625 + 9001.265625 = 9001.25
9001.265625 + -189.75z + z2 = 9001.25

Factor a perfect square on the left side:
(z + -94.875)(z + -94.875) = 9001.25

Calculate the square root of the right side: 94.874917655

Break this problem into two subproblems by setting 
(z + -94.875) equal to 94.874917655 and -94.874917655.


Subproblem 1
z + -94.875 = 94.874917655

Simplifying
z + -94.875 = 94.874917655

Reorder the terms:
-94.875 + z = 94.874917655

Solving
-94.875 + z = 94.874917655

Solving for variable 'z'.

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

Add '94.875' to each side of the equation.
-94.875 + 94.875 + z = 94.874917655 + 94.875

Combine like terms: -94.875 + 94.875 = 0.000
0.000 + z = 94.874917655 + 94.875
z = 94.874917655 + 94.875

Combine like terms: 94.874917655 + 94.875 = 189.749917655
z = 189.749917655

Simplifying
z = 189.749917655


Subproblem 2
z + -94.875 = -94.874917655

Simplifying
z + -94.875 = -94.874917655

Reorder the terms:
-94.875 + z = -94.874917655

Solving
-94.875 + z = -94.874917655

Solving for variable 'z'.

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

Add '94.875' to each side of the equation.
-94.875 + 94.875 + z = -94.874917655 + 94.875

Combine like terms: -94.875 + 94.875 = 0.000
0.000 + z = -94.874917655 + 94.875
z = -94.874917655 + 94.875

Combine like terms: -94.874917655 + 94.875 = 0.000082345
z = 0.000082345

Simplifying
z = 0.000082345


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {189.749917655, 0.000082345}

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