(x*x)-x=17

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Solution for (x*x)-x=17 equation: 


Simplifying
(x * x) + -1x = 17

Multiply x * x
(x2) + -1x = 17
x2 + -1x = 17

Reorder the terms:
-1x + x2 = 17

Solving
-1x + x2 = 17

Solving for variable 'x'.

Reorder the terms:
-17 + -1x + x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -1x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -1x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x + x2 = 0 + 17
-1x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
-1x + x2 = 17

The x term is -1x.  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.
-1x + 0.25 + x2 = 17 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 17 + 0.25

Combine like terms: 17 + 0.25 = 17.25
0.25 + -1x + x2 = 17.25

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

Calculate the square root of the right side: 4.153311931

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


Subproblem 1
x + -0.5 = 4.153311931

Simplifying
x + -0.5 = 4.153311931

Reorder the terms:
-0.5 + x = 4.153311931

Solving
-0.5 + x = 4.153311931

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 4.153311931 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 4.153311931 + 0.5
x = 4.153311931 + 0.5

Combine like terms: 4.153311931 + 0.5 = 4.653311931
x = 4.653311931

Simplifying
x = 4.653311931


Subproblem 2
x + -0.5 = -4.153311931

Simplifying
x + -0.5 = -4.153311931

Reorder the terms:
-0.5 + x = -4.153311931

Solving
-0.5 + x = -4.153311931

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -4.153311931 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -4.153311931 + 0.5
x = -4.153311931 + 0.5

Combine like terms: -4.153311931 + 0.5 = -3.653311931
x = -3.653311931

Simplifying
x = -3.653311931


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

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