0.2x(x+30)+0.2x=10

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Solution for 0.2x(x+30)+0.2x=10 equation: 


Simplifying
0.2x(x + 30) + 0.2x = 10

Reorder the terms:
0.2x(30 + x) + 0.2x = 10
(30 * 0.2x + x * 0.2x) + 0.2x = 10
(6x + 0.2x2) + 0.2x = 10

Reorder the terms:
6x + 0.2x + 0.2x2 = 10

Combine like terms: 6x + 0.2x = 6.2x
6.2x + 0.2x2 = 10

Solving
6.2x + 0.2x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 6.2x + 0.2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 6.2x + 0.2x2 = 0

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

Divide each side by '0.2'.
-50 + 31x + x2 = 0

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 31x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 31x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 31x + x2 = 0 + 50
31x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
31x + x2 = 50

The x term is 31x.  Take half its coefficient (15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
31x + 240.25 + x2 = 50 + 240.25

Reorder the terms:
240.25 + 31x + x2 = 50 + 240.25

Combine like terms: 50 + 240.25 = 290.25
240.25 + 31x + x2 = 290.25

Factor a perfect square on the left side:
(x + 15.5)(x + 15.5) = 290.25

Calculate the square root of the right side: 17.036725037

Break this problem into two subproblems by setting 
(x + 15.5) equal to 17.036725037 and -17.036725037.


Subproblem 1
x + 15.5 = 17.036725037

Simplifying
x + 15.5 = 17.036725037

Reorder the terms:
15.5 + x = 17.036725037

Solving
15.5 + x = 17.036725037

Solving for variable 'x'.

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

Add '-15.5' to each side of the equation.
15.5 + -15.5 + x = 17.036725037 + -15.5

Combine like terms: 15.5 + -15.5 = 0.0
0.0 + x = 17.036725037 + -15.5
x = 17.036725037 + -15.5

Combine like terms: 17.036725037 + -15.5 = 1.536725037
x = 1.536725037

Simplifying
x = 1.536725037


Subproblem 2
x + 15.5 = -17.036725037

Simplifying
x + 15.5 = -17.036725037

Reorder the terms:
15.5 + x = -17.036725037

Solving
15.5 + x = -17.036725037

Solving for variable 'x'.

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

Add '-15.5' to each side of the equation.
15.5 + -15.5 + x = -17.036725037 + -15.5

Combine like terms: 15.5 + -15.5 = 0.0
0.0 + x = -17.036725037 + -15.5
x = -17.036725037 + -15.5

Combine like terms: -17.036725037 + -15.5 = -32.536725037
x = -32.536725037

Simplifying
x = -32.536725037


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.536725037, -32.536725037}

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