0.0052x^2+0.13x-20=0

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Solution for 0.0052x^2+0.13x-20=0 equation: 


Simplifying
0.0052x2 + 0.13x + -20 = 0

Reorder the terms:
-20 + 0.13x + 0.0052x2 = 0

Solving
-20 + 0.13x + 0.0052x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.0052 the coefficient of the squared term: 

Divide each side by '0.0052'.
-3846.153846 + 25x + x2 = 0

Move the constant term to the right:

Add '3846.153846' to each side of the equation.
-3846.153846 + 25x + 3846.153846 + x2 = 0 + 3846.153846

Reorder the terms:
-3846.153846 + 3846.153846 + 25x + x2 = 0 + 3846.153846

Combine like terms: -3846.153846 + 3846.153846 = 0.000000
0.000000 + 25x + x2 = 0 + 3846.153846
25x + x2 = 0 + 3846.153846

Combine like terms: 0 + 3846.153846 = 3846.153846
25x + x2 = 3846.153846

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 3846.153846 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 3846.153846 + 156.25

Combine like terms: 3846.153846 + 156.25 = 4002.403846
156.25 + 25x + x2 = 4002.403846

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 4002.403846

Calculate the square root of the right side: 63.26455442

Break this problem into two subproblems by setting 
(x + 12.5) equal to 63.26455442 and -63.26455442.


Subproblem 1
x + 12.5 = 63.26455442

Simplifying
x + 12.5 = 63.26455442

Reorder the terms:
12.5 + x = 63.26455442

Solving
12.5 + x = 63.26455442

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 63.26455442 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 63.26455442 + -12.5
x = 63.26455442 + -12.5

Combine like terms: 63.26455442 + -12.5 = 50.76455442
x = 50.76455442

Simplifying
x = 50.76455442


Subproblem 2
x + 12.5 = -63.26455442

Simplifying
x + 12.5 = -63.26455442

Reorder the terms:
12.5 + x = -63.26455442

Solving
12.5 + x = -63.26455442

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -63.26455442 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -63.26455442 + -12.5
x = -63.26455442 + -12.5

Combine like terms: -63.26455442 + -12.5 = -75.76455442
x = -75.76455442

Simplifying
x = -75.76455442


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.76455442, -75.76455442}

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