4x^2-16x-1536=0

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Solution for 4x^2-16x-1536=0 equation: 


Simplifying
4x2 + -16x + -1536 = 0

Reorder the terms:
-1536 + -16x + 4x2 = 0

Solving
-1536 + -16x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-384 + -4x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-384 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-384 + -4x + x2 = 0

Solving
-384 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '384' to each side of the equation.
-384 + -4x + 384 + x2 = 0 + 384

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

Combine like terms: -384 + 384 = 0
0 + -4x + x2 = 0 + 384
-4x + x2 = 0 + 384

Combine like terms: 0 + 384 = 384
-4x + x2 = 384

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 384 + 4

Reorder the terms:
4 + -4x + x2 = 384 + 4

Combine like terms: 384 + 4 = 388
4 + -4x + x2 = 388

Factor a perfect square on the left side:
(x + -2)(x + -2) = 388

Calculate the square root of the right side: 19.697715604

Break this problem into two subproblems by setting 
(x + -2) equal to 19.697715604 and -19.697715604.


Subproblem 1
x + -2 = 19.697715604

Simplifying
x + -2 = 19.697715604

Reorder the terms:
-2 + x = 19.697715604

Solving
-2 + x = 19.697715604

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 19.697715604 + 2

Combine like terms: -2 + 2 = 0
0 + x = 19.697715604 + 2
x = 19.697715604 + 2

Combine like terms: 19.697715604 + 2 = 21.697715604
x = 21.697715604

Simplifying
x = 21.697715604


Subproblem 2
x + -2 = -19.697715604

Simplifying
x + -2 = -19.697715604

Reorder the terms:
-2 + x = -19.697715604

Solving
-2 + x = -19.697715604

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -19.697715604 + 2

Combine like terms: -2 + 2 = 0
0 + x = -19.697715604 + 2
x = -19.697715604 + 2

Combine like terms: -19.697715604 + 2 = -17.697715604
x = -17.697715604

Simplifying
x = -17.697715604


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.697715604, -17.697715604}
Solution
x = {21.697715604, -17.697715604}

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