(x^2)+24.1x-13.216=0

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Solution for (x^2)+24.1x-13.216=0 equation: 


Simplifying
(x2) + 24.1x + -13.216 = 0
x2 + 24.1x + -13.216 = 0

Reorder the terms:
-13.216 + 24.1x + x2 = 0

Solving
-13.216 + 24.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '13.216' to each side of the equation.
-13.216 + 24.1x + 13.216 + x2 = 0 + 13.216

Reorder the terms:
-13.216 + 13.216 + 24.1x + x2 = 0 + 13.216

Combine like terms: -13.216 + 13.216 = 0.000
0.000 + 24.1x + x2 = 0 + 13.216
24.1x + x2 = 0 + 13.216

Combine like terms: 0 + 13.216 = 13.216
24.1x + x2 = 13.216

The x term is 24.1x.  Take half its coefficient (12.05).
Square it (145.2025) and add it to both sides.

Add '145.2025' to each side of the equation.
24.1x + 145.2025 + x2 = 13.216 + 145.2025

Reorder the terms:
145.2025 + 24.1x + x2 = 13.216 + 145.2025

Combine like terms: 13.216 + 145.2025 = 158.4185
145.2025 + 24.1x + x2 = 158.4185

Factor a perfect square on the left side:
(x + 12.05)(x + 12.05) = 158.4185

Calculate the square root of the right side: 12.586441117

Break this problem into two subproblems by setting 
(x + 12.05) equal to 12.586441117 and -12.586441117.


Subproblem 1
x + 12.05 = 12.586441117

Simplifying
x + 12.05 = 12.586441117

Reorder the terms:
12.05 + x = 12.586441117

Solving
12.05 + x = 12.586441117

Solving for variable 'x'.

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

Add '-12.05' to each side of the equation.
12.05 + -12.05 + x = 12.586441117 + -12.05

Combine like terms: 12.05 + -12.05 = 0.00
0.00 + x = 12.586441117 + -12.05
x = 12.586441117 + -12.05

Combine like terms: 12.586441117 + -12.05 = 0.536441117
x = 0.536441117

Simplifying
x = 0.536441117


Subproblem 2
x + 12.05 = -12.586441117

Simplifying
x + 12.05 = -12.586441117

Reorder the terms:
12.05 + x = -12.586441117

Solving
12.05 + x = -12.586441117

Solving for variable 'x'.

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

Add '-12.05' to each side of the equation.
12.05 + -12.05 + x = -12.586441117 + -12.05

Combine like terms: 12.05 + -12.05 = 0.00
0.00 + x = -12.586441117 + -12.05
x = -12.586441117 + -12.05

Combine like terms: -12.586441117 + -12.05 = -24.636441117
x = -24.636441117

Simplifying
x = -24.636441117


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.536441117, -24.636441117}

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