4X^2+24X-48=0

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Solution for 4X^2+24X-48=0 equation: 


Simplifying
4X2 + 24X + -48 = 0

Reorder the terms:
-48 + 24X + 4X2 = 0

Solving
-48 + 24X + 4X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 6X + X2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-12 + 6X + X2)' equal to zero and attempt to solve:

Simplifying
-12 + 6X + X2 = 0

Solving
-12 + 6X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 6X + 12 + X2 = 0 + 12

Reorder the terms:
-12 + 12 + 6X + X2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 6X + X2 = 0 + 12
6X + X2 = 0 + 12

Combine like terms: 0 + 12 = 12
6X + X2 = 12

The X term is 6X.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6X + 9 + X2 = 12 + 9

Reorder the terms:
9 + 6X + X2 = 12 + 9

Combine like terms: 12 + 9 = 21
9 + 6X + X2 = 21

Factor a perfect square on the left side:
(X + 3)(X + 3) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(X + 3) equal to 4.582575695 and -4.582575695.


Subproblem 1
X + 3 = 4.582575695

Simplifying
X + 3 = 4.582575695

Reorder the terms:
3 + X = 4.582575695

Solving
3 + X = 4.582575695

Solving for variable 'X'.

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

Add '-3' to each side of the equation.
3 + -3 + X = 4.582575695 + -3

Combine like terms: 3 + -3 = 0
0 + X = 4.582575695 + -3
X = 4.582575695 + -3

Combine like terms: 4.582575695 + -3 = 1.582575695
X = 1.582575695

Simplifying
X = 1.582575695


Subproblem 2
X + 3 = -4.582575695

Simplifying
X + 3 = -4.582575695

Reorder the terms:
3 + X = -4.582575695

Solving
3 + X = -4.582575695

Solving for variable 'X'.

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

Add '-3' to each side of the equation.
3 + -3 + X = -4.582575695 + -3

Combine like terms: 3 + -3 = 0
0 + X = -4.582575695 + -3
X = -4.582575695 + -3

Combine like terms: -4.582575695 + -3 = -7.582575695
X = -7.582575695

Simplifying
X = -7.582575695


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.582575695, -7.582575695}
Solution
X = {1.582575695, -7.582575695}

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