0.089x^2+0.841x+1.224=0

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Solution for 0.089x^2+0.841x+1.224=0 equation: 


Simplifying
0.089x2 + 0.841x + 1.224 = 0

Reorder the terms:
1.224 + 0.841x + 0.089x2 = 0

Solving
1.224 + 0.841x + 0.089x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.089'.
13.75280899 + 9.449438202x + x2 = 0

Move the constant term to the right:

Add '-13.75280899' to each side of the equation.
13.75280899 + 9.449438202x + -13.75280899 + x2 = 0 + -13.75280899

Reorder the terms:
13.75280899 + -13.75280899 + 9.449438202x + x2 = 0 + -13.75280899

Combine like terms: 13.75280899 + -13.75280899 = 0.00000000
0.00000000 + 9.449438202x + x2 = 0 + -13.75280899
9.449438202x + x2 = 0 + -13.75280899

Combine like terms: 0 + -13.75280899 = -13.75280899
9.449438202x + x2 = -13.75280899

The x term is 9.449438202x.  Take half its coefficient (4.724719101).
Square it (22.32297058) and add it to both sides.

Add '22.32297058' to each side of the equation.
9.449438202x + 22.32297058 + x2 = -13.75280899 + 22.32297058

Reorder the terms:
22.32297058 + 9.449438202x + x2 = -13.75280899 + 22.32297058

Combine like terms: -13.75280899 + 22.32297058 = 8.57016159
22.32297058 + 9.449438202x + x2 = 8.57016159

Factor a perfect square on the left side:
(x + 4.724719101)(x + 4.724719101) = 8.57016159

Calculate the square root of the right side: 2.927483833

Break this problem into two subproblems by setting 
(x + 4.724719101) equal to 2.927483833 and -2.927483833.


Subproblem 1
x + 4.724719101 = 2.927483833

Simplifying
x + 4.724719101 = 2.927483833

Reorder the terms:
4.724719101 + x = 2.927483833

Solving
4.724719101 + x = 2.927483833

Solving for variable 'x'.

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

Add '-4.724719101' to each side of the equation.
4.724719101 + -4.724719101 + x = 2.927483833 + -4.724719101

Combine like terms: 4.724719101 + -4.724719101 = 0.000000000
0.000000000 + x = 2.927483833 + -4.724719101
x = 2.927483833 + -4.724719101

Combine like terms: 2.927483833 + -4.724719101 = -1.797235268
x = -1.797235268

Simplifying
x = -1.797235268


Subproblem 2
x + 4.724719101 = -2.927483833

Simplifying
x + 4.724719101 = -2.927483833

Reorder the terms:
4.724719101 + x = -2.927483833

Solving
4.724719101 + x = -2.927483833

Solving for variable 'x'.

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

Add '-4.724719101' to each side of the equation.
4.724719101 + -4.724719101 + x = -2.927483833 + -4.724719101

Combine like terms: 4.724719101 + -4.724719101 = 0.000000000
0.000000000 + x = -2.927483833 + -4.724719101
x = -2.927483833 + -4.724719101

Combine like terms: -2.927483833 + -4.724719101 = -7.652202934
x = -7.652202934

Simplifying
x = -7.652202934


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.797235268, -7.652202934}

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