-0.11x^2+0.49x+1=0

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Solution for -0.11x^2+0.49x+1=0 equation: 


Simplifying
-0.11x2 + 0.49x + 1 = 0

Reorder the terms:
1 + 0.49x + -0.11x2 = 0

Solving
1 + 0.49x + -0.11x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.11 the coefficient of the squared term: 

Divide each side by '-0.11'.
-9.090909091 + -4.454545455x + x2 = 0

Move the constant term to the right:

Add '9.090909091' to each side of the equation.
-9.090909091 + -4.454545455x + 9.090909091 + x2 = 0 + 9.090909091

Reorder the terms:
-9.090909091 + 9.090909091 + -4.454545455x + x2 = 0 + 9.090909091

Combine like terms: -9.090909091 + 9.090909091 = 0.000000000
0.000000000 + -4.454545455x + x2 = 0 + 9.090909091
-4.454545455x + x2 = 0 + 9.090909091

Combine like terms: 0 + 9.090909091 = 9.090909091
-4.454545455x + x2 = 9.090909091

The x term is -4.454545455x.  Take half its coefficient (-2.227272728).
Square it (4.960743805) and add it to both sides.

Add '4.960743805' to each side of the equation.
-4.454545455x + 4.960743805 + x2 = 9.090909091 + 4.960743805

Reorder the terms:
4.960743805 + -4.454545455x + x2 = 9.090909091 + 4.960743805

Combine like terms: 9.090909091 + 4.960743805 = 14.051652896
4.960743805 + -4.454545455x + x2 = 14.051652896

Factor a perfect square on the left side:
(x + -2.227272728)(x + -2.227272728) = 14.051652896

Calculate the square root of the right side: 3.74855344

Break this problem into two subproblems by setting 
(x + -2.227272728) equal to 3.74855344 and -3.74855344.


Subproblem 1
x + -2.227272728 = 3.74855344

Simplifying
x + -2.227272728 = 3.74855344

Reorder the terms:
-2.227272728 + x = 3.74855344

Solving
-2.227272728 + x = 3.74855344

Solving for variable 'x'.

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

Add '2.227272728' to each side of the equation.
-2.227272728 + 2.227272728 + x = 3.74855344 + 2.227272728

Combine like terms: -2.227272728 + 2.227272728 = 0.000000000
0.000000000 + x = 3.74855344 + 2.227272728
x = 3.74855344 + 2.227272728

Combine like terms: 3.74855344 + 2.227272728 = 5.975826168
x = 5.975826168

Simplifying
x = 5.975826168


Subproblem 2
x + -2.227272728 = -3.74855344

Simplifying
x + -2.227272728 = -3.74855344

Reorder the terms:
-2.227272728 + x = -3.74855344

Solving
-2.227272728 + x = -3.74855344

Solving for variable 'x'.

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

Add '2.227272728' to each side of the equation.
-2.227272728 + 2.227272728 + x = -3.74855344 + 2.227272728

Combine like terms: -2.227272728 + 2.227272728 = 0.000000000
0.000000000 + x = -3.74855344 + 2.227272728
x = -3.74855344 + 2.227272728

Combine like terms: -3.74855344 + 2.227272728 = -1.521280712
x = -1.521280712

Simplifying
x = -1.521280712


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.975826168, -1.521280712}

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