2x*(x+1)=576

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Solution for 2x*(x+1)=576 equation: 


Simplifying
2x(x + 1) = 576

Reorder the terms:
2x(1 + x) = 576
(1 * 2x + x * 2x) = 576
(2x + 2x2) = 576

Solving
2x + 2x2 = 576

Solving for variable 'x'.

Reorder the terms:
-576 + 2x + 2x2 = 576 + -576

Combine like terms: 576 + -576 = 0
-576 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-288 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-288 + x + x2)' equal to zero and attempt to solve:

Simplifying
-288 + x + x2 = 0

Solving
-288 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '288' to each side of the equation.
-288 + x + 288 + x2 = 0 + 288

Reorder the terms:
-288 + 288 + x + x2 = 0 + 288

Combine like terms: -288 + 288 = 0
0 + x + x2 = 0 + 288
x + x2 = 0 + 288

Combine like terms: 0 + 288 = 288
x + x2 = 288

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 288 + 0.25

Reorder the terms:
0.25 + x + x2 = 288 + 0.25

Combine like terms: 288 + 0.25 = 288.25
0.25 + x + x2 = 288.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 288.25

Calculate the square root of the right side: 16.977926846

Break this problem into two subproblems by setting 
(x + 0.5) equal to 16.977926846 and -16.977926846.


Subproblem 1
x + 0.5 = 16.977926846

Simplifying
x + 0.5 = 16.977926846

Reorder the terms:
0.5 + x = 16.977926846

Solving
0.5 + x = 16.977926846

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 16.977926846 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 16.977926846 + -0.5
x = 16.977926846 + -0.5

Combine like terms: 16.977926846 + -0.5 = 16.477926846
x = 16.477926846

Simplifying
x = 16.477926846


Subproblem 2
x + 0.5 = -16.977926846

Simplifying
x + 0.5 = -16.977926846

Reorder the terms:
0.5 + x = -16.977926846

Solving
0.5 + x = -16.977926846

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -16.977926846 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -16.977926846 + -0.5
x = -16.977926846 + -0.5

Combine like terms: -16.977926846 + -0.5 = -17.477926846
x = -17.477926846

Simplifying
x = -17.477926846


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.477926846, -17.477926846}
Solution
x = {16.477926846, -17.477926846}

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