x^2+0.883x-0.229=0

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Solution for x^2+0.883x-0.229=0 equation:


Simplifying
x2 + 0.883x + -0.229 = 0

Reorder the terms:
-0.229 + 0.883x + x2 = 0

Solving
-0.229 + 0.883x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.229' to each side of the equation.
-0.229 + 0.883x + 0.229 + x2 = 0 + 0.229

Reorder the terms:
-0.229 + 0.229 + 0.883x + x2 = 0 + 0.229

Combine like terms: -0.229 + 0.229 = 0.000
0.000 + 0.883x + x2 = 0 + 0.229
0.883x + x2 = 0 + 0.229

Combine like terms: 0 + 0.229 = 0.229
0.883x + x2 = 0.229

The x term is 0.883x.  Take half its coefficient (0.4415).
Square it (0.19492225) and add it to both sides.

Add '0.19492225' to each side of the equation.
0.883x + 0.19492225 + x2 = 0.229 + 0.19492225

Reorder the terms:
0.19492225 + 0.883x + x2 = 0.229 + 0.19492225

Combine like terms: 0.229 + 0.19492225 = 0.42392225
0.19492225 + 0.883x + x2 = 0.42392225

Factor a perfect square on the left side:
(x + 0.4415)(x + 0.4415) = 0.42392225

Calculate the square root of the right side: 0.651093119

Break this problem into two subproblems by setting 
(x + 0.4415) equal to 0.651093119 and -0.651093119.


Subproblem 1
x + 0.4415 = 0.651093119

Simplifying
x + 0.4415 = 0.651093119

Reorder the terms:
0.4415 + x = 0.651093119

Solving
0.4415 + x = 0.651093119

Solving for variable 'x'.

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

Add '-0.4415' to each side of the equation.
0.4415 + -0.4415 + x = 0.651093119 + -0.4415

Combine like terms: 0.4415 + -0.4415 = 0.0000
0.0000 + x = 0.651093119 + -0.4415
x = 0.651093119 + -0.4415

Combine like terms: 0.651093119 + -0.4415 = 0.209593119
x = 0.209593119

Simplifying
x = 0.209593119


Subproblem 2
x + 0.4415 = -0.651093119

Simplifying
x + 0.4415 = -0.651093119

Reorder the terms:
0.4415 + x = -0.651093119

Solving
0.4415 + x = -0.651093119

Solving for variable 'x'.

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

Add '-0.4415' to each side of the equation.
0.4415 + -0.4415 + x = -0.651093119 + -0.4415

Combine like terms: 0.4415 + -0.4415 = 0.0000
0.0000 + x = -0.651093119 + -0.4415
x = -0.651093119 + -0.4415

Combine like terms: -0.651093119 + -0.4415 = -1.092593119
x = -1.092593119

Simplifying
x = -1.092593119


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.209593119, -1.092593119}

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