z^2-z=17

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Solution for z^2-z=17 equation:


Simplifying
z2 + -1z = 17

Reorder the terms:
-1z + z2 = 17

Solving
-1z + z2 = 17

Solving for variable 'z'.

Reorder the terms:
-17 + -1z + z2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + -1z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -1z + 17 + z2 = 0 + 17

Reorder the terms:
-17 + 17 + -1z + z2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1z + z2 = 0 + 17
-1z + z2 = 0 + 17

Combine like terms: 0 + 17 = 17
-1z + z2 = 17

The z term is -1z.  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 = 17 + 0.25

Reorder the terms:
0.25 + -1z + z2 = 17 + 0.25

Combine like terms: 17 + 0.25 = 17.25
0.25 + -1z + z2 = 17.25

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(z + -0.5) equal to 4.153311931 and -4.153311931.

Subproblem 1

z + -0.5 = 4.153311931 Simplifying z + -0.5 = 4.153311931 Reorder the terms: -0.5 + z = 4.153311931 Solving -0.5 + z = 4.153311931 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 = 4.153311931 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = 4.153311931 + 0.5 z = 4.153311931 + 0.5 Combine like terms: 4.153311931 + 0.5 = 4.653311931 z = 4.653311931 Simplifying z = 4.653311931

Subproblem 2

z + -0.5 = -4.153311931 Simplifying z + -0.5 = -4.153311931 Reorder the terms: -0.5 + z = -4.153311931 Solving -0.5 + z = -4.153311931 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 = -4.153311931 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = -4.153311931 + 0.5 z = -4.153311931 + 0.5 Combine like terms: -4.153311931 + 0.5 = -3.653311931 z = -3.653311931 Simplifying z = -3.653311931

Solution

The solution to the problem is based on the solutions from the subproblems. z = {4.653311931, -3.653311931}

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