Z^2-16Z=15

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Solution for Z^2-16Z=15 equation: 


Simplifying
Z2 + -16Z = 15

Reorder the terms:
-16Z + Z2 = 15

Solving
-16Z + Z2 = 15

Solving for variable 'Z'.

Reorder the terms:
-15 + -16Z + Z2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -16Z + Z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -16Z + 15 + Z2 = 0 + 15

Reorder the terms:
-15 + 15 + -16Z + Z2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -16Z + Z2 = 0 + 15
-16Z + Z2 = 0 + 15

Combine like terms: 0 + 15 = 15
-16Z + Z2 = 15

The Z term is -16Z.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16Z + 64 + Z2 = 15 + 64

Reorder the terms:
64 + -16Z + Z2 = 15 + 64

Combine like terms: 15 + 64 = 79
64 + -16Z + Z2 = 79

Factor a perfect square on the left side:
(Z + -8)(Z + -8) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(Z + -8) equal to 8.888194417 and -8.888194417.


Subproblem 1
Z + -8 = 8.888194417

Simplifying
Z + -8 = 8.888194417

Reorder the terms:
-8 + Z = 8.888194417

Solving
-8 + Z = 8.888194417

Solving for variable 'Z'.

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

Add '8' to each side of the equation.
-8 + 8 + Z = 8.888194417 + 8

Combine like terms: -8 + 8 = 0
0 + Z = 8.888194417 + 8
Z = 8.888194417 + 8

Combine like terms: 8.888194417 + 8 = 16.888194417
Z = 16.888194417

Simplifying
Z = 16.888194417


Subproblem 2
Z + -8 = -8.888194417

Simplifying
Z + -8 = -8.888194417

Reorder the terms:
-8 + Z = -8.888194417

Solving
-8 + Z = -8.888194417

Solving for variable 'Z'.

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

Add '8' to each side of the equation.
-8 + 8 + Z = -8.888194417 + 8

Combine like terms: -8 + 8 = 0
0 + Z = -8.888194417 + 8
Z = -8.888194417 + 8

Combine like terms: -8.888194417 + 8 = -0.888194417
Z = -0.888194417

Simplifying
Z = -0.888194417


Solution
The solution to the problem is based on the solutions
from the subproblems.
Z = {16.888194417, -0.888194417}

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