x^2+20x-19.8=x

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Solution for x^2+20x-19.8=x equation: 


Simplifying
x2 + 20x + -19.8 = x

Reorder the terms:
-19.8 + 20x + x2 = x

Solving
-19.8 + 20x + x2 = x

Solving for variable 'x'.

Reorder the terms:
-19.8 + 20x + -1x + x2 = x + -1x

Combine like terms: 20x + -1x = 19x
-19.8 + 19x + x2 = x + -1x

Combine like terms: x + -1x = 0
-19.8 + 19x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19.8' to each side of the equation.
-19.8 + 19x + 19.8 + x2 = 0 + 19.8

Reorder the terms:
-19.8 + 19.8 + 19x + x2 = 0 + 19.8

Combine like terms: -19.8 + 19.8 = 0.0
0.0 + 19x + x2 = 0 + 19.8
19x + x2 = 0 + 19.8

Combine like terms: 0 + 19.8 = 19.8
19x + x2 = 19.8

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = 19.8 + 90.25

Reorder the terms:
90.25 + 19x + x2 = 19.8 + 90.25

Combine like terms: 19.8 + 90.25 = 110.05
90.25 + 19x + x2 = 110.05

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 110.05

Calculate the square root of the right side: 10.490471867

Break this problem into two subproblems by setting 
(x + 9.5) equal to 10.490471867 and -10.490471867.


Subproblem 1
x + 9.5 = 10.490471867

Simplifying
x + 9.5 = 10.490471867

Reorder the terms:
9.5 + x = 10.490471867

Solving
9.5 + x = 10.490471867

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 10.490471867 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 10.490471867 + -9.5
x = 10.490471867 + -9.5

Combine like terms: 10.490471867 + -9.5 = 0.990471867
x = 0.990471867

Simplifying
x = 0.990471867


Subproblem 2
x + 9.5 = -10.490471867

Simplifying
x + 9.5 = -10.490471867

Reorder the terms:
9.5 + x = -10.490471867

Solving
9.5 + x = -10.490471867

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = -10.490471867 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -10.490471867 + -9.5
x = -10.490471867 + -9.5

Combine like terms: -10.490471867 + -9.5 = -19.990471867
x = -19.990471867

Simplifying
x = -19.990471867


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.990471867, -19.990471867}

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