.11111x^2-x-3=0

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Solution for .11111x^2-x-3=0 equation: 


Simplifying
0.11111x2 + -1x + -3 = 0

Reorder the terms:
-3 + -1x + 0.11111x2 = 0

Solving
-3 + -1x + 0.11111x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.11111 the coefficient of the squared term: 

Divide each side by '0.11111'.
-27.00027 + -9.000090001x + x2 = 0

Move the constant term to the right:

Add '27.00027' to each side of the equation.
-27.00027 + -9.000090001x + 27.00027 + x2 = 0 + 27.00027

Reorder the terms:
-27.00027 + 27.00027 + -9.000090001x + x2 = 0 + 27.00027

Combine like terms: -27.00027 + 27.00027 = 0.00000
0.00000 + -9.000090001x + x2 = 0 + 27.00027
-9.000090001x + x2 = 0 + 27.00027

Combine like terms: 0 + 27.00027 = 27.00027
-9.000090001x + x2 = 27.00027

The x term is -9.000090001x.  Take half its coefficient (-4.500045001).
Square it (20.25040501) and add it to both sides.

Add '20.25040501' to each side of the equation.
-9.000090001x + 20.25040501 + x2 = 27.00027 + 20.25040501

Reorder the terms:
20.25040501 + -9.000090001x + x2 = 27.00027 + 20.25040501

Combine like terms: 27.00027 + 20.25040501 = 47.25067501
20.25040501 + -9.000090001x + x2 = 47.25067501

Factor a perfect square on the left side:
(x + -4.500045001)(x + -4.500045001) = 47.25067501

Calculate the square root of the right side: 6.873912642

Break this problem into two subproblems by setting 
(x + -4.500045001) equal to 6.873912642 and -6.873912642.


Subproblem 1
x + -4.500045001 = 6.873912642

Simplifying
x + -4.500045001 = 6.873912642

Reorder the terms:
-4.500045001 + x = 6.873912642

Solving
-4.500045001 + x = 6.873912642

Solving for variable 'x'.

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

Add '4.500045001' to each side of the equation.
-4.500045001 + 4.500045001 + x = 6.873912642 + 4.500045001

Combine like terms: -4.500045001 + 4.500045001 = 0.000000000
0.000000000 + x = 6.873912642 + 4.500045001
x = 6.873912642 + 4.500045001

Combine like terms: 6.873912642 + 4.500045001 = 11.373957643
x = 11.373957643

Simplifying
x = 11.373957643


Subproblem 2
x + -4.500045001 = -6.873912642

Simplifying
x + -4.500045001 = -6.873912642

Reorder the terms:
-4.500045001 + x = -6.873912642

Solving
-4.500045001 + x = -6.873912642

Solving for variable 'x'.

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

Add '4.500045001' to each side of the equation.
-4.500045001 + 4.500045001 + x = -6.873912642 + 4.500045001

Combine like terms: -4.500045001 + 4.500045001 = 0.000000000
0.000000000 + x = -6.873912642 + 4.500045001
x = -6.873912642 + 4.500045001

Combine like terms: -6.873912642 + 4.500045001 = -2.373867641
x = -2.373867641

Simplifying
x = -2.373867641


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.373957643, -2.373867641}

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