Z^2-2Z+0.75=0

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Solution for Z^2-2Z+0.75=0 equation:


Simplifying
Z2 + -2Z + 0.75 = 0

Reorder the terms:
0.75 + -2Z + Z2 = 0

Solving
0.75 + -2Z + Z2 = 0

Solving for variable 'Z'.

Begin completing the square.

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -2Z + -0.75 + Z2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -2Z + Z2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2Z + Z2 = 0 + -0.75
-2Z + Z2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-2Z + Z2 = -0.75

The Z term is -2Z.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2Z + 1 + Z2 = -0.75 + 1

Reorder the terms:
1 + -2Z + Z2 = -0.75 + 1

Combine like terms: -0.75 + 1 = 0.25
1 + -2Z + Z2 = 0.25

Factor a perfect square on the left side:
(Z + -1)(Z + -1) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(Z + -1) equal to 0.5 and -0.5.

Subproblem 1

Z + -1 = 0.5 Simplifying Z + -1 = 0.5 Reorder the terms: -1 + Z = 0.5 Solving -1 + Z = 0.5 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + Z = 0.5 + 1 Combine like terms: -1 + 1 = 0 0 + Z = 0.5 + 1 Z = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 Z = 1.5 Simplifying Z = 1.5

Subproblem 2

Z + -1 = -0.5 Simplifying Z + -1 = -0.5 Reorder the terms: -1 + Z = -0.5 Solving -1 + Z = -0.5 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + Z = -0.5 + 1 Combine like terms: -1 + 1 = 0 0 + Z = -0.5 + 1 Z = -0.5 + 1 Combine like terms: -0.5 + 1 = 0.5 Z = 0.5 Simplifying Z = 0.5

Solution

The solution to the problem is based on the solutions from the subproblems. Z = {1.5, 0.5}

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