2(x^2+3x-432)=0

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Solution for 2(x^2+3x-432)=0 equation: 


Simplifying
2(x2 + 3x + -432) = 0

Reorder the terms:
2(-432 + 3x + x2) = 0
(-432 * 2 + 3x * 2 + x2 * 2) = 0
(-864 + 6x + 2x2) = 0

Solving
-864 + 6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-432 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-432 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-432 + 3x + x2 = 0

Solving
-432 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '432' to each side of the equation.
-432 + 3x + 432 + x2 = 0 + 432

Reorder the terms:
-432 + 432 + 3x + x2 = 0 + 432

Combine like terms: -432 + 432 = 0
0 + 3x + x2 = 0 + 432
3x + x2 = 0 + 432

Combine like terms: 0 + 432 = 432
3x + x2 = 432

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 = 432 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 432 + 2.25

Combine like terms: 432 + 2.25 = 434.25
2.25 + 3x + x2 = 434.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 434.25

Calculate the square root of the right side: 20.838665984

Break this problem into two subproblems by setting 
(x + 1.5) equal to 20.838665984 and -20.838665984.


Subproblem 1
x + 1.5 = 20.838665984

Simplifying
x + 1.5 = 20.838665984

Reorder the terms:
1.5 + x = 20.838665984

Solving
1.5 + x = 20.838665984

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 = 20.838665984 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 20.838665984 + -1.5
x = 20.838665984 + -1.5

Combine like terms: 20.838665984 + -1.5 = 19.338665984
x = 19.338665984

Simplifying
x = 19.338665984


Subproblem 2
x + 1.5 = -20.838665984

Simplifying
x + 1.5 = -20.838665984

Reorder the terms:
1.5 + x = -20.838665984

Solving
1.5 + x = -20.838665984

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 = -20.838665984 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -20.838665984 + -1.5
x = -20.838665984 + -1.5

Combine like terms: -20.838665984 + -1.5 = -22.338665984
x = -22.338665984

Simplifying
x = -22.338665984


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.338665984, -22.338665984}
Solution
x = {19.338665984, -22.338665984}

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