192=x(x+2+4)

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Solution for 192=x(x+2+4) equation:


Simplifying
192 = x(x + 2 + 4)

Reorder the terms:
192 = x(2 + 4 + x)

Combine like terms: 2 + 4 = 6
192 = x(6 + x)
192 = (6 * x + x * x)
192 = (6x + x2)

Solving
192 = 6x + x2

Solving for variable 'x'.

Reorder the terms:
192 + -6x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
192 + -6x + -1x2 = 0 + x2 + -1x2
192 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
192 + -6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-192 + 6x + x2 = 0

Move the constant term to the right:

Add '192' to each side of the equation.
-192 + 6x + 192 + x2 = 0 + 192

Reorder the terms:
-192 + 192 + 6x + x2 = 0 + 192

Combine like terms: -192 + 192 = 0
0 + 6x + x2 = 0 + 192
6x + x2 = 0 + 192

Combine like terms: 0 + 192 = 192
6x + x2 = 192

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 = 192 + 9

Reorder the terms:
9 + 6x + x2 = 192 + 9

Combine like terms: 192 + 9 = 201
9 + 6x + x2 = 201

Factor a perfect square on the left side:
(x + 3)(x + 3) = 201

Calculate the square root of the right side: 14.177446879

Break this problem into two subproblems by setting 
(x + 3) equal to 14.177446879 and -14.177446879.

Subproblem 1

x + 3 = 14.177446879 Simplifying x + 3 = 14.177446879 Reorder the terms: 3 + x = 14.177446879 Solving 3 + x = 14.177446879 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 = 14.177446879 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.177446879 + -3 x = 14.177446879 + -3 Combine like terms: 14.177446879 + -3 = 11.177446879 x = 11.177446879 Simplifying x = 11.177446879

Subproblem 2

x + 3 = -14.177446879 Simplifying x + 3 = -14.177446879 Reorder the terms: 3 + x = -14.177446879 Solving 3 + x = -14.177446879 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 = -14.177446879 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.177446879 + -3 x = -14.177446879 + -3 Combine like terms: -14.177446879 + -3 = -17.177446879 x = -17.177446879 Simplifying x = -17.177446879

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.177446879, -17.177446879}

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