2x(x+3)=24

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Solution for 2x(x+3)=24 equation: 


Simplifying
2x(x + 3) = 24

Reorder the terms:
2x(3 + x) = 24
(3 * 2x + x * 2x) = 24
(6x + 2x2) = 24

Solving
6x + 2x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 6x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-12 + 3x + x2 = 0

Solving
-12 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 3x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 3x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 3x + x2 = 0 + 12
3x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
3x + x2 = 12

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 = 12 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 12 + 2.25

Combine like terms: 12 + 2.25 = 14.25
2.25 + 3x + x2 = 14.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
x + 1.5 = 3.774917218

Simplifying
x + 1.5 = 3.774917218

Reorder the terms:
1.5 + x = 3.774917218

Solving
1.5 + x = 3.774917218

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 = 3.774917218 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.774917218 + -1.5
x = 3.774917218 + -1.5

Combine like terms: 3.774917218 + -1.5 = 2.274917218
x = 2.274917218

Simplifying
x = 2.274917218


Subproblem 2
x + 1.5 = -3.774917218

Simplifying
x + 1.5 = -3.774917218

Reorder the terms:
1.5 + x = -3.774917218

Solving
1.5 + x = -3.774917218

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 = -3.774917218 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.774917218 + -1.5
x = -3.774917218 + -1.5

Combine like terms: -3.774917218 + -1.5 = -5.274917218
x = -5.274917218

Simplifying
x = -5.274917218


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.274917218, -5.274917218}
Solution
x = {2.274917218, -5.274917218}

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