(x+16)x=364

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Solution for (x+16)x=364 equation: 


Simplifying
(x + 16) * x = 364

Reorder the terms:
(16 + x) * x = 364

Reorder the terms for easier multiplication:
x(16 + x) = 364
(16 * x + x * x) = 364
(16x + x2) = 364

Solving
16x + x2 = 364

Solving for variable 'x'.

Reorder the terms:
-364 + 16x + x2 = 364 + -364

Combine like terms: 364 + -364 = 0
-364 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '364' to each side of the equation.
-364 + 16x + 364 + x2 = 0 + 364

Reorder the terms:
-364 + 364 + 16x + x2 = 0 + 364

Combine like terms: -364 + 364 = 0
0 + 16x + x2 = 0 + 364
16x + x2 = 0 + 364

Combine like terms: 0 + 364 = 364
16x + x2 = 364

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 364 + 64

Reorder the terms:
64 + 16x + x2 = 364 + 64

Combine like terms: 364 + 64 = 428
64 + 16x + x2 = 428

Factor a perfect square on the left side:
(x + 8)(x + 8) = 428

Calculate the square root of the right side: 20.688160866

Break this problem into two subproblems by setting 
(x + 8) equal to 20.688160866 and -20.688160866.


Subproblem 1
x + 8 = 20.688160866

Simplifying
x + 8 = 20.688160866

Reorder the terms:
8 + x = 20.688160866

Solving
8 + x = 20.688160866

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 20.688160866 + -8

Combine like terms: 8 + -8 = 0
0 + x = 20.688160866 + -8
x = 20.688160866 + -8

Combine like terms: 20.688160866 + -8 = 12.688160866
x = 12.688160866

Simplifying
x = 12.688160866


Subproblem 2
x + 8 = -20.688160866

Simplifying
x + 8 = -20.688160866

Reorder the terms:
8 + x = -20.688160866

Solving
8 + x = -20.688160866

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -20.688160866 + -8

Combine like terms: 8 + -8 = 0
0 + x = -20.688160866 + -8
x = -20.688160866 + -8

Combine like terms: -20.688160866 + -8 = -28.688160866
x = -28.688160866

Simplifying
x = -28.688160866


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.688160866, -28.688160866}

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