x^2-x=0.833

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Solution for x^2-x=0.833 equation: 


Simplifying
x2 + -1x = 0.833

Reorder the terms:
-1x + x2 = 0.833

Solving
-1x + x2 = 0.833

Solving for variable 'x'.

Reorder the terms:
-0.833 + -1x + x2 = 0.833 + -0.833

Combine like terms: 0.833 + -0.833 = 0.000
-0.833 + -1x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.833' to each side of the equation.
-0.833 + -1x + 0.833 + x2 = 0.000 + 0.833

Reorder the terms:
-0.833 + 0.833 + -1x + x2 = 0.000 + 0.833

Combine like terms: -0.833 + 0.833 = 0.000
0.000 + -1x + x2 = 0.000 + 0.833
-1x + x2 = 0.000 + 0.833

Combine like terms: 0.000 + 0.833 = 0.833
-1x + x2 = 0.833

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 = 0.833 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.833 + 0.25

Combine like terms: 0.833 + 0.25 = 1.083
0.25 + -1x + x2 = 1.083

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.083

Calculate the square root of the right side: 1.040672859

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.040672859 and -1.040672859.


Subproblem 1
x + -0.5 = 1.040672859

Simplifying
x + -0.5 = 1.040672859

Reorder the terms:
-0.5 + x = 1.040672859

Solving
-0.5 + x = 1.040672859

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 = 1.040672859 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.040672859 + 0.5
x = 1.040672859 + 0.5

Combine like terms: 1.040672859 + 0.5 = 1.540672859
x = 1.540672859

Simplifying
x = 1.540672859


Subproblem 2
x + -0.5 = -1.040672859

Simplifying
x + -0.5 = -1.040672859

Reorder the terms:
-0.5 + x = -1.040672859

Solving
-0.5 + x = -1.040672859

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 = -1.040672859 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.040672859 + 0.5
x = -1.040672859 + 0.5

Combine like terms: -1.040672859 + 0.5 = -0.540672859
x = -0.540672859

Simplifying
x = -0.540672859


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.540672859, -0.540672859}

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