x(x+0.3)=5.6

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Solution for x(x+0.3)=5.6 equation: 


Simplifying
x(x + 0.3) = 5.6

Reorder the terms:
x(0.3 + x) = 5.6
(0.3 * x + x * x) = 5.6
(0.3x + x2) = 5.6

Solving
0.3x + x2 = 5.6

Solving for variable 'x'.

Reorder the terms:
-5.6 + 0.3x + x2 = 5.6 + -5.6

Combine like terms: 5.6 + -5.6 = 0.0
-5.6 + 0.3x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '5.6' to each side of the equation.
-5.6 + 0.3x + 5.6 + x2 = 0.0 + 5.6

Reorder the terms:
-5.6 + 5.6 + 0.3x + x2 = 0.0 + 5.6

Combine like terms: -5.6 + 5.6 = 0.0
0.0 + 0.3x + x2 = 0.0 + 5.6
0.3x + x2 = 0.0 + 5.6

Combine like terms: 0.0 + 5.6 = 5.6
0.3x + x2 = 5.6

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 = 5.6 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 5.6 + 0.0225

Combine like terms: 5.6 + 0.0225 = 5.6225
0.0225 + 0.3x + x2 = 5.6225

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 5.6225

Calculate the square root of the right side: 2.37118114

Break this problem into two subproblems by setting 
(x + 0.15) equal to 2.37118114 and -2.37118114.


Subproblem 1
x + 0.15 = 2.37118114

Simplifying
x + 0.15 = 2.37118114

Reorder the terms:
0.15 + x = 2.37118114

Solving
0.15 + x = 2.37118114

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 = 2.37118114 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = 2.37118114 + -0.15
x = 2.37118114 + -0.15

Combine like terms: 2.37118114 + -0.15 = 2.22118114
x = 2.22118114

Simplifying
x = 2.22118114


Subproblem 2
x + 0.15 = -2.37118114

Simplifying
x + 0.15 = -2.37118114

Reorder the terms:
0.15 + x = -2.37118114

Solving
0.15 + x = -2.37118114

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 = -2.37118114 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = -2.37118114 + -0.15
x = -2.37118114 + -0.15

Combine like terms: -2.37118114 + -0.15 = -2.52118114
x = -2.52118114

Simplifying
x = -2.52118114


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.22118114, -2.52118114}

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