0.0911+1.0454x+x^2=0

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Solution for 0.0911+1.0454x+x^2=0 equation: 


Simplifying
0.0911 + 1.0454x + x2 = 0

Solving
0.0911 + 1.0454x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.0911' to each side of the equation.
0.0911 + 1.0454x + -0.0911 + x2 = 0 + -0.0911

Reorder the terms:
0.0911 + -0.0911 + 1.0454x + x2 = 0 + -0.0911

Combine like terms: 0.0911 + -0.0911 = 0.0000
0.0000 + 1.0454x + x2 = 0 + -0.0911
1.0454x + x2 = 0 + -0.0911

Combine like terms: 0 + -0.0911 = -0.0911
1.0454x + x2 = -0.0911

The x term is 1.0454x.  Take half its coefficient (0.5227).
Square it (0.27321529) and add it to both sides.

Add '0.27321529' to each side of the equation.
1.0454x + 0.27321529 + x2 = -0.0911 + 0.27321529

Reorder the terms:
0.27321529 + 1.0454x + x2 = -0.0911 + 0.27321529

Combine like terms: -0.0911 + 0.27321529 = 0.18211529
0.27321529 + 1.0454x + x2 = 0.18211529

Factor a perfect square on the left side:
(x + 0.5227)(x + 0.5227) = 0.18211529

Calculate the square root of the right side: 0.426749681

Break this problem into two subproblems by setting 
(x + 0.5227) equal to 0.426749681 and -0.426749681.


Subproblem 1
x + 0.5227 = 0.426749681

Simplifying
x + 0.5227 = 0.426749681

Reorder the terms:
0.5227 + x = 0.426749681

Solving
0.5227 + x = 0.426749681

Solving for variable 'x'.

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

Add '-0.5227' to each side of the equation.
0.5227 + -0.5227 + x = 0.426749681 + -0.5227

Combine like terms: 0.5227 + -0.5227 = 0.0000
0.0000 + x = 0.426749681 + -0.5227
x = 0.426749681 + -0.5227

Combine like terms: 0.426749681 + -0.5227 = -0.095950319
x = -0.095950319

Simplifying
x = -0.095950319


Subproblem 2
x + 0.5227 = -0.426749681

Simplifying
x + 0.5227 = -0.426749681

Reorder the terms:
0.5227 + x = -0.426749681

Solving
0.5227 + x = -0.426749681

Solving for variable 'x'.

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

Add '-0.5227' to each side of the equation.
0.5227 + -0.5227 + x = -0.426749681 + -0.5227

Combine like terms: 0.5227 + -0.5227 = 0.0000
0.0000 + x = -0.426749681 + -0.5227
x = -0.426749681 + -0.5227

Combine like terms: -0.426749681 + -0.5227 = -0.949449681
x = -0.949449681

Simplifying
x = -0.949449681


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.095950319, -0.949449681}

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