x^2+4.1x-12=0

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Solution for x^2+4.1x-12=0 equation: 


Simplifying
x2 + 4.1x + -12 = 0

Reorder the terms:
-12 + 4.1x + x2 = 0

Solving
-12 + 4.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 4.1x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 4.1x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 4.1x + x2 = 0 + 12
4.1x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
4.1x + x2 = 12

The x term is 4.1x.  Take half its coefficient (2.05).
Square it (4.2025) and add it to both sides.

Add '4.2025' to each side of the equation.
4.1x + 4.2025 + x2 = 12 + 4.2025

Reorder the terms:
4.2025 + 4.1x + x2 = 12 + 4.2025

Combine like terms: 12 + 4.2025 = 16.2025
4.2025 + 4.1x + x2 = 16.2025

Factor a perfect square on the left side:
(x + 2.05)(x + 2.05) = 16.2025

Calculate the square root of the right side: 4.025232913

Break this problem into two subproblems by setting 
(x + 2.05) equal to 4.025232913 and -4.025232913.


Subproblem 1
x + 2.05 = 4.025232913

Simplifying
x + 2.05 = 4.025232913

Reorder the terms:
2.05 + x = 4.025232913

Solving
2.05 + x = 4.025232913

Solving for variable 'x'.

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

Add '-2.05' to each side of the equation.
2.05 + -2.05 + x = 4.025232913 + -2.05

Combine like terms: 2.05 + -2.05 = 0.00
0.00 + x = 4.025232913 + -2.05
x = 4.025232913 + -2.05

Combine like terms: 4.025232913 + -2.05 = 1.975232913
x = 1.975232913

Simplifying
x = 1.975232913


Subproblem 2
x + 2.05 = -4.025232913

Simplifying
x + 2.05 = -4.025232913

Reorder the terms:
2.05 + x = -4.025232913

Solving
2.05 + x = -4.025232913

Solving for variable 'x'.

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

Add '-2.05' to each side of the equation.
2.05 + -2.05 + x = -4.025232913 + -2.05

Combine like terms: 2.05 + -2.05 = 0.00
0.00 + x = -4.025232913 + -2.05
x = -4.025232913 + -2.05

Combine like terms: -4.025232913 + -2.05 = -6.075232913
x = -6.075232913

Simplifying
x = -6.075232913


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.975232913, -6.075232913}

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