20-5x+0.15x^2=0

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Solution for 20-5x+0.15x^2=0 equation: 


Simplifying
20 + -5x + 0.15x2 = 0

Solving
20 + -5x + 0.15x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.15'.
133.3333333 + -33.33333333x + x2 = 0

Move the constant term to the right:

Add '-133.3333333' to each side of the equation.
133.3333333 + -33.33333333x + -133.3333333 + x2 = 0 + -133.3333333

Reorder the terms:
133.3333333 + -133.3333333 + -33.33333333x + x2 = 0 + -133.3333333

Combine like terms: 133.3333333 + -133.3333333 = 0.0000000
0.0000000 + -33.33333333x + x2 = 0 + -133.3333333
-33.33333333x + x2 = 0 + -133.3333333

Combine like terms: 0 + -133.3333333 = -133.3333333
-33.33333333x + x2 = -133.3333333

The x term is -33.33333333x.  Take half its coefficient (-16.66666667).
Square it (277.7777779) and add it to both sides.

Add '277.7777779' to each side of the equation.
-33.33333333x + 277.7777779 + x2 = -133.3333333 + 277.7777779

Reorder the terms:
277.7777779 + -33.33333333x + x2 = -133.3333333 + 277.7777779

Combine like terms: -133.3333333 + 277.7777779 = 144.4444446
277.7777779 + -33.33333333x + x2 = 144.4444446

Factor a perfect square on the left side:
(x + -16.66666667)(x + -16.66666667) = 144.4444446

Calculate the square root of the right side: 12.018504258

Break this problem into two subproblems by setting 
(x + -16.66666667) equal to 12.018504258 and -12.018504258.


Subproblem 1
x + -16.66666667 = 12.018504258

Simplifying
x + -16.66666667 = 12.018504258

Reorder the terms:
-16.66666667 + x = 12.018504258

Solving
-16.66666667 + x = 12.018504258

Solving for variable 'x'.

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

Add '16.66666667' to each side of the equation.
-16.66666667 + 16.66666667 + x = 12.018504258 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + x = 12.018504258 + 16.66666667
x = 12.018504258 + 16.66666667

Combine like terms: 12.018504258 + 16.66666667 = 28.685170928
x = 28.685170928

Simplifying
x = 28.685170928


Subproblem 2
x + -16.66666667 = -12.018504258

Simplifying
x + -16.66666667 = -12.018504258

Reorder the terms:
-16.66666667 + x = -12.018504258

Solving
-16.66666667 + x = -12.018504258

Solving for variable 'x'.

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

Add '16.66666667' to each side of the equation.
-16.66666667 + 16.66666667 + x = -12.018504258 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + x = -12.018504258 + 16.66666667
x = -12.018504258 + 16.66666667

Combine like terms: -12.018504258 + 16.66666667 = 4.648162412
x = 4.648162412

Simplifying
x = 4.648162412


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.685170928, 4.648162412}

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