2x(x)+56x+192=396

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Solution for 2x(x)+56x+192=396 equation: 


Simplifying
2x(x) + 56x + 192 = 396

Multiply x * x
2x2 + 56x + 192 = 396

Reorder the terms:
192 + 56x + 2x2 = 396

Solving
192 + 56x + 2x2 = 396

Solving for variable 'x'.

Reorder the terms:
192 + -396 + 56x + 2x2 = 396 + -396

Combine like terms: 192 + -396 = -204
-204 + 56x + 2x2 = 396 + -396

Combine like terms: 396 + -396 = 0
-204 + 56x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-102 + 28x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-102 + 28x + x2)' equal to zero and attempt to solve:

Simplifying
-102 + 28x + x2 = 0

Solving
-102 + 28x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '102' to each side of the equation.
-102 + 28x + 102 + x2 = 0 + 102

Reorder the terms:
-102 + 102 + 28x + x2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + 28x + x2 = 0 + 102
28x + x2 = 0 + 102

Combine like terms: 0 + 102 = 102
28x + x2 = 102

The x term is 28x.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28x + 196 + x2 = 102 + 196

Reorder the terms:
196 + 28x + x2 = 102 + 196

Combine like terms: 102 + 196 = 298
196 + 28x + x2 = 298

Factor a perfect square on the left side:
(x + 14)(x + 14) = 298

Calculate the square root of the right side: 17.262676502

Break this problem into two subproblems by setting 
(x + 14) equal to 17.262676502 and -17.262676502.


Subproblem 1
x + 14 = 17.262676502

Simplifying
x + 14 = 17.262676502

Reorder the terms:
14 + x = 17.262676502

Solving
14 + x = 17.262676502

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + x = 17.262676502 + -14

Combine like terms: 14 + -14 = 0
0 + x = 17.262676502 + -14
x = 17.262676502 + -14

Combine like terms: 17.262676502 + -14 = 3.262676502
x = 3.262676502

Simplifying
x = 3.262676502


Subproblem 2
x + 14 = -17.262676502

Simplifying
x + 14 = -17.262676502

Reorder the terms:
14 + x = -17.262676502

Solving
14 + x = -17.262676502

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + x = -17.262676502 + -14

Combine like terms: 14 + -14 = 0
0 + x = -17.262676502 + -14
x = -17.262676502 + -14

Combine like terms: -17.262676502 + -14 = -31.262676502
x = -31.262676502

Simplifying
x = -31.262676502


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.262676502, -31.262676502}
Solution
x = {3.262676502, -31.262676502}

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