3x(x+3)=24

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


Simplifying
3x(x + 3) = 24

Reorder the terms:
3x(3 + x) = 24
(3 * 3x + x * 3x) = 24
(9x + 3x2) = 24

Solving
9x + 3x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 9x + 3x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 3x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + 3x + x2 = 0

Solving
-8 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 3x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 3x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x + x2 = 0 + 8
3x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
3x + x2 = 8

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 = 8 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + 3x + x2 = 10.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x + 1.5 = 3.201562119

Simplifying
x + 1.5 = 3.201562119

Reorder the terms:
1.5 + x = 3.201562119

Solving
1.5 + x = 3.201562119

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 = 3.201562119 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.201562119 + -1.5
x = 3.201562119 + -1.5

Combine like terms: 3.201562119 + -1.5 = 1.701562119
x = 1.701562119

Simplifying
x = 1.701562119


Subproblem 2
x + 1.5 = -3.201562119

Simplifying
x + 1.5 = -3.201562119

Reorder the terms:
1.5 + x = -3.201562119

Solving
1.5 + x = -3.201562119

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 = -3.201562119 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.201562119 + -1.5
x = -3.201562119 + -1.5

Combine like terms: -3.201562119 + -1.5 = -4.701562119
x = -4.701562119

Simplifying
x = -4.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.701562119, -4.701562119}
Solution
x = {1.701562119, -4.701562119}

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