4x^2+384x+96=0

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Solution for 4x^2+384x+96=0 equation: 


Simplifying
4x2 + 384x + 96 = 0

Reorder the terms:
96 + 384x + 4x2 = 0

Solving
96 + 384x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(24 + 96x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(24 + 96x + x2)' equal to zero and attempt to solve:

Simplifying
24 + 96x + x2 = 0

Solving
24 + 96x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + 96x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + 96x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 96x + x2 = 0 + -24
96x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
96x + x2 = -24

The x term is 96x.  Take half its coefficient (48).
Square it (2304) and add it to both sides.

Add '2304' to each side of the equation.
96x + 2304 + x2 = -24 + 2304

Reorder the terms:
2304 + 96x + x2 = -24 + 2304

Combine like terms: -24 + 2304 = 2280
2304 + 96x + x2 = 2280

Factor a perfect square on the left side:
(x + 48)(x + 48) = 2280

Calculate the square root of the right side: 47.749345545

Break this problem into two subproblems by setting 
(x + 48) equal to 47.749345545 and -47.749345545.


Subproblem 1
x + 48 = 47.749345545

Simplifying
x + 48 = 47.749345545

Reorder the terms:
48 + x = 47.749345545

Solving
48 + x = 47.749345545

Solving for variable 'x'.

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

Add '-48' to each side of the equation.
48 + -48 + x = 47.749345545 + -48

Combine like terms: 48 + -48 = 0
0 + x = 47.749345545 + -48
x = 47.749345545 + -48

Combine like terms: 47.749345545 + -48 = -0.250654455
x = -0.250654455

Simplifying
x = -0.250654455


Subproblem 2
x + 48 = -47.749345545

Simplifying
x + 48 = -47.749345545

Reorder the terms:
48 + x = -47.749345545

Solving
48 + x = -47.749345545

Solving for variable 'x'.

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

Add '-48' to each side of the equation.
48 + -48 + x = -47.749345545 + -48

Combine like terms: 48 + -48 = 0
0 + x = -47.749345545 + -48
x = -47.749345545 + -48

Combine like terms: -47.749345545 + -48 = -95.749345545
x = -95.749345545

Simplifying
x = -95.749345545


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.250654455, -95.749345545}
Solution
x = {-0.250654455, -95.749345545}

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