x(x+0.15)=0.045

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Solution for x(x+0.15)=0.045 equation: 


Simplifying
x(x + 0.15) = 0.045

Reorder the terms:
x(0.15 + x) = 0.045
(0.15 * x + x * x) = 0.045
(0.15x + x2) = 0.045

Solving
0.15x + x2 = 0.045

Solving for variable 'x'.

Reorder the terms:
-0.045 + 0.15x + x2 = 0.045 + -0.045

Combine like terms: 0.045 + -0.045 = 0.000
-0.045 + 0.15x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.045' to each side of the equation.
-0.045 + 0.15x + 0.045 + x2 = 0.000 + 0.045

Reorder the terms:
-0.045 + 0.045 + 0.15x + x2 = 0.000 + 0.045

Combine like terms: -0.045 + 0.045 = 0.000
0.000 + 0.15x + x2 = 0.000 + 0.045
0.15x + x2 = 0.000 + 0.045

Combine like terms: 0.000 + 0.045 = 0.045
0.15x + x2 = 0.045

The x term is 0.15x.  Take half its coefficient (0.075).
Square it (0.005625) and add it to both sides.

Add '0.005625' to each side of the equation.
0.15x + 0.005625 + x2 = 0.045 + 0.005625

Reorder the terms:
0.005625 + 0.15x + x2 = 0.045 + 0.005625

Combine like terms: 0.045 + 0.005625 = 0.050625
0.005625 + 0.15x + x2 = 0.050625

Factor a perfect square on the left side:
(x + 0.075)(x + 0.075) = 0.050625

Calculate the square root of the right side: 0.225

Break this problem into two subproblems by setting 
(x + 0.075) equal to 0.225 and -0.225.


Subproblem 1
x + 0.075 = 0.225

Simplifying
x + 0.075 = 0.225

Reorder the terms:
0.075 + x = 0.225

Solving
0.075 + x = 0.225

Solving for variable 'x'.

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

Add '-0.075' to each side of the equation.
0.075 + -0.075 + x = 0.225 + -0.075

Combine like terms: 0.075 + -0.075 = 0.000
0.000 + x = 0.225 + -0.075
x = 0.225 + -0.075

Combine like terms: 0.225 + -0.075 = 0.15
x = 0.15

Simplifying
x = 0.15


Subproblem 2
x + 0.075 = -0.225

Simplifying
x + 0.075 = -0.225

Reorder the terms:
0.075 + x = -0.225

Solving
0.075 + x = -0.225

Solving for variable 'x'.

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

Add '-0.075' to each side of the equation.
0.075 + -0.075 + x = -0.225 + -0.075

Combine like terms: 0.075 + -0.075 = 0.000
0.000 + x = -0.225 + -0.075
x = -0.225 + -0.075

Combine like terms: -0.225 + -0.075 = -0.3
x = -0.3

Simplifying
x = -0.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.15, -0.3}

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