x(x+0.3)=180

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Solution for x(x+0.3)=180 equation: 


Simplifying
x(x + 0.3) = 180

Reorder the terms:
x(0.3 + x) = 180
(0.3 * x + x * x) = 180
(0.3x + x2) = 180

Solving
0.3x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 0.3x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 0.3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 0.3x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + 0.3x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 0.3x + x2 = 0 + 180
0.3x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
0.3x + x2 = 180

The x term is 0.3x.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3x + 0.0225 + x2 = 180 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 180 + 0.0225

Combine like terms: 180 + 0.0225 = 180.0225
0.0225 + 0.3x + x2 = 180.0225

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 180.0225

Calculate the square root of the right side: 13.417246364

Break this problem into two subproblems by setting 
(x + 0.15) equal to 13.417246364 and -13.417246364.


Subproblem 1
x + 0.15 = 13.417246364

Simplifying
x + 0.15 = 13.417246364

Reorder the terms:
0.15 + x = 13.417246364

Solving
0.15 + x = 13.417246364

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = 13.417246364 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = 13.417246364 + -0.15
x = 13.417246364 + -0.15

Combine like terms: 13.417246364 + -0.15 = 13.267246364
x = 13.267246364

Simplifying
x = 13.267246364


Subproblem 2
x + 0.15 = -13.417246364

Simplifying
x + 0.15 = -13.417246364

Reorder the terms:
0.15 + x = -13.417246364

Solving
0.15 + x = -13.417246364

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = -13.417246364 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = -13.417246364 + -0.15
x = -13.417246364 + -0.15

Combine like terms: -13.417246364 + -0.15 = -13.567246364
x = -13.567246364

Simplifying
x = -13.567246364


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.267246364, -13.567246364}

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