x(x+0.6)=500

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Solution for x(x+0.6)=500 equation: 


Simplifying
x(x + 0.6) = 500

Reorder the terms:
x(0.6 + x) = 500
(0.6 * x + x * x) = 500
(0.6x + x2) = 500

Solving
0.6x + x2 = 500

Solving for variable 'x'.

Reorder the terms:
-500 + 0.6x + x2 = 500 + -500

Combine like terms: 500 + -500 = 0
-500 + 0.6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '500' to each side of the equation.
-500 + 0.6x + 500 + x2 = 0 + 500

Reorder the terms:
-500 + 500 + 0.6x + x2 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + 0.6x + x2 = 0 + 500
0.6x + x2 = 0 + 500

Combine like terms: 0 + 500 = 500
0.6x + x2 = 500

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 500 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 500 + 0.09

Combine like terms: 500 + 0.09 = 500.09
0.09 + 0.6x + x2 = 500.09

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 500.09

Calculate the square root of the right side: 22.362692146

Break this problem into two subproblems by setting 
(x + 0.3) equal to 22.362692146 and -22.362692146.


Subproblem 1
x + 0.3 = 22.362692146

Simplifying
x + 0.3 = 22.362692146

Reorder the terms:
0.3 + x = 22.362692146

Solving
0.3 + x = 22.362692146

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = 22.362692146 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 22.362692146 + -0.3
x = 22.362692146 + -0.3

Combine like terms: 22.362692146 + -0.3 = 22.062692146
x = 22.062692146

Simplifying
x = 22.062692146


Subproblem 2
x + 0.3 = -22.362692146

Simplifying
x + 0.3 = -22.362692146

Reorder the terms:
0.3 + x = -22.362692146

Solving
0.3 + x = -22.362692146

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = -22.362692146 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -22.362692146 + -0.3
x = -22.362692146 + -0.3

Combine like terms: -22.362692146 + -0.3 = -22.662692146
x = -22.662692146

Simplifying
x = -22.662692146


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.062692146, -22.662692146}

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