(2x+11)x=1600

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Solution for (2x+11)x=1600 equation: 


Simplifying
(2x + 11) * x = 1600

Reorder the terms:
(11 + 2x) * x = 1600

Reorder the terms for easier multiplication:
x(11 + 2x) = 1600
(11 * x + 2x * x) = 1600
(11x + 2x2) = 1600

Solving
11x + 2x2 = 1600

Solving for variable 'x'.

Reorder the terms:
-1600 + 11x + 2x2 = 1600 + -1600

Combine like terms: 1600 + -1600 = 0
-1600 + 11x + 2x2 = 0

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

Divide each side by '2'.
-800 + 5.5x + x2 = 0

Move the constant term to the right:

Add '800' to each side of the equation.
-800 + 5.5x + 800 + x2 = 0 + 800

Reorder the terms:
-800 + 800 + 5.5x + x2 = 0 + 800

Combine like terms: -800 + 800 = 0
0 + 5.5x + x2 = 0 + 800
5.5x + x2 = 0 + 800

Combine like terms: 0 + 800 = 800
5.5x + x2 = 800

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = 800 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 800 + 7.5625

Combine like terms: 800 + 7.5625 = 807.5625
7.5625 + 5.5x + x2 = 807.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 807.5625

Calculate the square root of the right side: 28.417644167

Break this problem into two subproblems by setting 
(x + 2.75) equal to 28.417644167 and -28.417644167.


Subproblem 1
x + 2.75 = 28.417644167

Simplifying
x + 2.75 = 28.417644167

Reorder the terms:
2.75 + x = 28.417644167

Solving
2.75 + x = 28.417644167

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 28.417644167 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 28.417644167 + -2.75
x = 28.417644167 + -2.75

Combine like terms: 28.417644167 + -2.75 = 25.667644167
x = 25.667644167

Simplifying
x = 25.667644167


Subproblem 2
x + 2.75 = -28.417644167

Simplifying
x + 2.75 = -28.417644167

Reorder the terms:
2.75 + x = -28.417644167

Solving
2.75 + x = -28.417644167

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -28.417644167 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -28.417644167 + -2.75
x = -28.417644167 + -2.75

Combine like terms: -28.417644167 + -2.75 = -31.167644167
x = -31.167644167

Simplifying
x = -31.167644167


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.667644167, -31.167644167}

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