x(2x+6)=600

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Solution for x(2x+6)=600 equation: 


Simplifying
x(2x + 6) = 600

Reorder the terms:
x(6 + 2x) = 600
(6 * x + 2x * x) = 600
(6x + 2x2) = 600

Solving
6x + 2x2 = 600

Solving for variable 'x'.

Reorder the terms:
-600 + 6x + 2x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-600 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-300 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-300 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-300 + 3x + x2 = 0

Solving
-300 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 3x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + 3x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 3x + x2 = 0 + 300
3x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
3x + x2 = 300

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 300 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 300 + 2.25

Combine like terms: 300 + 2.25 = 302.25
2.25 + 3x + x2 = 302.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 302.25

Calculate the square root of the right side: 17.385338651

Break this problem into two subproblems by setting 
(x + 1.5) equal to 17.385338651 and -17.385338651.


Subproblem 1
x + 1.5 = 17.385338651

Simplifying
x + 1.5 = 17.385338651

Reorder the terms:
1.5 + x = 17.385338651

Solving
1.5 + x = 17.385338651

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 17.385338651 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 17.385338651 + -1.5
x = 17.385338651 + -1.5

Combine like terms: 17.385338651 + -1.5 = 15.885338651
x = 15.885338651

Simplifying
x = 15.885338651


Subproblem 2
x + 1.5 = -17.385338651

Simplifying
x + 1.5 = -17.385338651

Reorder the terms:
1.5 + x = -17.385338651

Solving
1.5 + x = -17.385338651

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -17.385338651 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -17.385338651 + -1.5
x = -17.385338651 + -1.5

Combine like terms: -17.385338651 + -1.5 = -18.885338651
x = -18.885338651

Simplifying
x = -18.885338651


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.885338651, -18.885338651}
Solution
x = {15.885338651, -18.885338651}

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