(z-12)(z-12)=55

Solution for (z-12)(z-12)=55 equation:

Simplifying
(z + -12)(z + -12) = 55

Reorder the terms:
(-12 + z)(z + -12) = 55

Reorder the terms:
(-12 + z)(-12 + z) = 55

Multiply (-12 + z) * (-12 + z)
(-12(-12 + z) + z(-12 + z)) = 55
((-12 * -12 + z * -12) + z(-12 + z)) = 55
((144 + -12z) + z(-12 + z)) = 55
(144 + -12z + (-12 * z + z * z)) = 55
(144 + -12z + (-12z + z2)) = 55

Combine like terms: -12z + -12z = -24z
(144 + -24z + z2) = 55

Solving
144 + -24z + z2 = 55

Solving for variable 'z'.

Reorder the terms:
144 + -55 + -24z + z2 = 55 + -55

Combine like terms: 144 + -55 = 89
89 + -24z + z2 = 55 + -55

Combine like terms: 55 + -55 = 0
89 + -24z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-89' to each side of the equation.
89 + -24z + -89 + z2 = 0 + -89

Reorder the terms:
89 + -89 + -24z + z2 = 0 + -89

Combine like terms: 89 + -89 = 0
0 + -24z + z2 = 0 + -89
-24z + z2 = 0 + -89

Combine like terms: 0 + -89 = -89
-24z + z2 = -89

The z term is -24z.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24z + 144 + z2 = -89 + 144

Reorder the terms:
144 + -24z + z2 = -89 + 144

Combine like terms: -89 + 144 = 55
144 + -24z + z2 = 55

Factor a perfect square on the left side:
(z + -12)(z + -12) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(z + -12) equal to 7.416198487 and -7.416198487.

Subproblem 1
z + -12 = 7.416198487

Simplifying
z + -12 = 7.416198487

Reorder the terms:
-12 + z = 7.416198487

Solving
-12 + z = 7.416198487

Solving for variable 'z'.

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

Add '12' to each side of the equation.
-12 + 12 + z = 7.416198487 + 12

Combine like terms: -12 + 12 = 0
0 + z = 7.416198487 + 12
z = 7.416198487 + 12

Combine like terms: 7.416198487 + 12 = 19.416198487
z = 19.416198487

Simplifying
z = 19.416198487

Subproblem 2
z + -12 = -7.416198487

Simplifying
z + -12 = -7.416198487

Reorder the terms:
-12 + z = -7.416198487

Solving
-12 + z = -7.416198487

Solving for variable 'z'.

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

Add '12' to each side of the equation.
-12 + 12 + z = -7.416198487 + 12

Combine like terms: -12 + 12 = 0
0 + z = -7.416198487 + 12
z = -7.416198487 + 12

Combine like terms: -7.416198487 + 12 = 4.583801513
z = 4.583801513

Simplifying
z = 4.583801513

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {19.416198487, 4.583801513}