x^2-4x-384=0

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Solution for x^2-4x-384=0 equation:


Simplifying
x2 + -4x + -384 = 0

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

Solving
-384 + -4x + x2 = 0

Solving for variable 'x'.

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}

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