20.4=20x+4.9x^2

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Solution for 20.4=20x+4.9x^2 equation: 


Simplifying
20.4 = 20x + 4.9x2

Solving
20.4 = 20x + 4.9x2

Solving for variable 'x'.

Reorder the terms:
20.4 + -20x + -4.9x2 = 20x + -20x + 4.9x2 + -4.9x2

Combine like terms: 20x + -20x = 0
20.4 + -20x + -4.9x2 = 0 + 4.9x2 + -4.9x2
20.4 + -20x + -4.9x2 = 4.9x2 + -4.9x2

Combine like terms: 4.9x2 + -4.9x2 = 0.0
20.4 + -20x + -4.9x2 = 0.0

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-4.163265306 + 4.081632653x + x2 = 0

Move the constant term to the right:

Add '4.163265306' to each side of the equation.
-4.163265306 + 4.081632653x + 4.163265306 + x2 = 0 + 4.163265306

Reorder the terms:
-4.163265306 + 4.163265306 + 4.081632653x + x2 = 0 + 4.163265306

Combine like terms: -4.163265306 + 4.163265306 = 0.000000000
0.000000000 + 4.081632653x + x2 = 0 + 4.163265306
4.081632653x + x2 = 0 + 4.163265306

Combine like terms: 0 + 4.163265306 = 4.163265306
4.081632653x + x2 = 4.163265306

The x term is 4.081632653x.  Take half its coefficient (2.040816327).
Square it (4.164931281) and add it to both sides.

Add '4.164931281' to each side of the equation.
4.081632653x + 4.164931281 + x2 = 4.163265306 + 4.164931281

Reorder the terms:
4.164931281 + 4.081632653x + x2 = 4.163265306 + 4.164931281

Combine like terms: 4.163265306 + 4.164931281 = 8.328196587
4.164931281 + 4.081632653x + x2 = 8.328196587

Factor a perfect square on the left side:
(x + 2.040816327)(x + 2.040816327) = 8.328196587

Calculate the square root of the right side: 2.885861498

Break this problem into two subproblems by setting 
(x + 2.040816327) equal to 2.885861498 and -2.885861498.


Subproblem 1
x + 2.040816327 = 2.885861498

Simplifying
x + 2.040816327 = 2.885861498

Reorder the terms:
2.040816327 + x = 2.885861498

Solving
2.040816327 + x = 2.885861498

Solving for variable 'x'.

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

Add '-2.040816327' to each side of the equation.
2.040816327 + -2.040816327 + x = 2.885861498 + -2.040816327

Combine like terms: 2.040816327 + -2.040816327 = 0.000000000
0.000000000 + x = 2.885861498 + -2.040816327
x = 2.885861498 + -2.040816327

Combine like terms: 2.885861498 + -2.040816327 = 0.845045171
x = 0.845045171

Simplifying
x = 0.845045171


Subproblem 2
x + 2.040816327 = -2.885861498

Simplifying
x + 2.040816327 = -2.885861498

Reorder the terms:
2.040816327 + x = -2.885861498

Solving
2.040816327 + x = -2.885861498

Solving for variable 'x'.

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

Add '-2.040816327' to each side of the equation.
2.040816327 + -2.040816327 + x = -2.885861498 + -2.040816327

Combine like terms: 2.040816327 + -2.040816327 = 0.000000000
0.000000000 + x = -2.885861498 + -2.040816327
x = -2.885861498 + -2.040816327

Combine like terms: -2.885861498 + -2.040816327 = -4.926677825
x = -4.926677825

Simplifying
x = -4.926677825


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.845045171, -4.926677825}

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