0.3x^2+x=40

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Solution for 0.3x^2+x=40 equation: 


Simplifying
0.3x2 + x = 40

Reorder the terms:
x + 0.3x2 = 40

Solving
x + 0.3x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + x + 0.3x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + x + 0.3x2 = 0

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

Divide each side by '0.3'.
-133.3333333 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '133.3333333' to each side of the equation.
-133.3333333 + 3.333333333x + 133.3333333 + x2 = 0 + 133.3333333

Reorder the terms:
-133.3333333 + 133.3333333 + 3.333333333x + x2 = 0 + 133.3333333

Combine like terms: -133.3333333 + 133.3333333 = 0.0000000
0.0000000 + 3.333333333x + x2 = 0 + 133.3333333
3.333333333x + x2 = 0 + 133.3333333

Combine like terms: 0 + 133.3333333 = 133.3333333
3.333333333x + x2 = 133.3333333

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.
3.333333333x + 0.25 + x2 = 133.3333333 + 0.25

Reorder the terms:
0.25 + 3.333333333x + x2 = 133.3333333 + 0.25

Combine like terms: 133.3333333 + 0.25 = 133.5833333
0.25 + 3.333333333x + x2 = 133.5833333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 133.5833333

Calculate the square root of the right side: 11.55782563

Break this problem into two subproblems by setting 
(x + 0.5) equal to 11.55782563 and -11.55782563.


Subproblem 1
x + 0.5 = 11.55782563

Simplifying
x + 0.5 = 11.55782563

Reorder the terms:
0.5 + x = 11.55782563

Solving
0.5 + x = 11.55782563

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 = 11.55782563 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 11.55782563 + -0.5
x = 11.55782563 + -0.5

Combine like terms: 11.55782563 + -0.5 = 11.05782563
x = 11.05782563

Simplifying
x = 11.05782563


Subproblem 2
x + 0.5 = -11.55782563

Simplifying
x + 0.5 = -11.55782563

Reorder the terms:
0.5 + x = -11.55782563

Solving
0.5 + x = -11.55782563

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 = -11.55782563 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -11.55782563 + -0.5
x = -11.55782563 + -0.5

Combine like terms: -11.55782563 + -0.5 = -12.05782563
x = -12.05782563

Simplifying
x = -12.05782563


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.05782563, -12.05782563}

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