-0.5x^2+x+20.62=0

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Solution for -0.5x^2+x+20.62=0 equation: 


Simplifying
-0.5x2 + x + 20.62 = 0

Reorder the terms:
20.62 + x + -0.5x2 = 0

Solving
20.62 + x + -0.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-41.24 + -2x + x2 = 0

Move the constant term to the right:

Add '41.24' to each side of the equation.
-41.24 + -2x + 41.24 + x2 = 0 + 41.24

Reorder the terms:
-41.24 + 41.24 + -2x + x2 = 0 + 41.24

Combine like terms: -41.24 + 41.24 = 0.00
0.00 + -2x + x2 = 0 + 41.24
-2x + x2 = 0 + 41.24

Combine like terms: 0 + 41.24 = 41.24
-2x + x2 = 41.24

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-2x + 0.25 + x2 = 41.24 + 0.25

Reorder the terms:
0.25 + -2x + x2 = 41.24 + 0.25

Combine like terms: 41.24 + 0.25 = 41.49
0.25 + -2x + x2 = 41.49

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 41.49

Calculate the square root of the right side: 6.441273166

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.441273166 and -6.441273166.


Subproblem 1
x + 0.5 = 6.441273166

Simplifying
x + 0.5 = 6.441273166

Reorder the terms:
0.5 + x = 6.441273166

Solving
0.5 + x = 6.441273166

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 6.441273166 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 6.441273166 + -0.5
x = 6.441273166 + -0.5

Combine like terms: 6.441273166 + -0.5 = 5.941273166
x = 5.941273166

Simplifying
x = 5.941273166


Subproblem 2
x + 0.5 = -6.441273166

Simplifying
x + 0.5 = -6.441273166

Reorder the terms:
0.5 + x = -6.441273166

Solving
0.5 + x = -6.441273166

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -6.441273166 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -6.441273166 + -0.5
x = -6.441273166 + -0.5

Combine like terms: -6.441273166 + -0.5 = -6.941273166
x = -6.941273166

Simplifying
x = -6.941273166


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.941273166, -6.941273166}

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