z-z^2=0.25

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Solution for z-z^2=0.25 equation:


Simplifying
z + -1z2 = 0.25

Solving
z + -1z2 = 0.25

Solving for variable 'z'.

Reorder the terms:
-0.25 + z + -1z2 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + z + -1z2 = 0.00

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
0.25 + -1z + z2 = 0.00

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1z + -0.25 + z2 = 0.00 + -0.25

Reorder the terms:
0.25 + -0.25 + -1z + z2 = 0.00 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1z + z2 = 0.00 + -0.25
-1z + z2 = 0.00 + -0.25

Combine like terms: 0.00 + -0.25 = -0.25
-1z + z2 = -0.25

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1z + 0.25 + z2 = -0.25 + 0.25

Reorder the terms:
0.25 + -1z + z2 = -0.25 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.25 + -1z + z2 = 0.00

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(z + 0.5) equal to 0.00 and 0.00.

Subproblem 1

z + 0.5 = 0.00 Simplifying z + 0.5 = 0.00 Reorder the terms: 0.5 + z = 0.00 Solving 0.5 + z = 0.00 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = 0.00 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 0.00 + -0.5 z = 0.00 + -0.5 Combine like terms: 0.00 + -0.5 = -0.5 z = -0.5 Simplifying z = -0.5

Subproblem 2

z + 0.5 = 0.00 Simplifying z + 0.5 = 0.00 Reorder the terms: 0.5 + z = 0.00 Solving 0.5 + z = 0.00 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = 0.00 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 0.00 + -0.5 z = 0.00 + -0.5 Combine like terms: 0.00 + -0.5 = -0.5 z = -0.5 Simplifying z = -0.5

Solution

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

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