(11+x)(16+x)=324

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Solution for (11+x)(16+x)=324 equation: 


Simplifying
(11 + x)(16 + x) = 324

Multiply (11 + x) * (16 + x)
(11(16 + x) + x(16 + x)) = 324
((16 * 11 + x * 11) + x(16 + x)) = 324
((176 + 11x) + x(16 + x)) = 324
(176 + 11x + (16 * x + x * x)) = 324
(176 + 11x + (16x + x2)) = 324

Combine like terms: 11x + 16x = 27x
(176 + 27x + x2) = 324

Solving
176 + 27x + x2 = 324

Solving for variable 'x'.

Reorder the terms:
176 + -324 + 27x + x2 = 324 + -324

Combine like terms: 176 + -324 = -148
-148 + 27x + x2 = 324 + -324

Combine like terms: 324 + -324 = 0
-148 + 27x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '148' to each side of the equation.
-148 + 27x + 148 + x2 = 0 + 148

Reorder the terms:
-148 + 148 + 27x + x2 = 0 + 148

Combine like terms: -148 + 148 = 0
0 + 27x + x2 = 0 + 148
27x + x2 = 0 + 148

Combine like terms: 0 + 148 = 148
27x + x2 = 148

The x term is 27x.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27x + 182.25 + x2 = 148 + 182.25

Reorder the terms:
182.25 + 27x + x2 = 148 + 182.25

Combine like terms: 148 + 182.25 = 330.25
182.25 + 27x + x2 = 330.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 330.25

Calculate the square root of the right side: 18.172781845

Break this problem into two subproblems by setting 
(x + 13.5) equal to 18.172781845 and -18.172781845.


Subproblem 1
x + 13.5 = 18.172781845

Simplifying
x + 13.5 = 18.172781845

Reorder the terms:
13.5 + x = 18.172781845

Solving
13.5 + x = 18.172781845

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = 18.172781845 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = 18.172781845 + -13.5
x = 18.172781845 + -13.5

Combine like terms: 18.172781845 + -13.5 = 4.672781845
x = 4.672781845

Simplifying
x = 4.672781845


Subproblem 2
x + 13.5 = -18.172781845

Simplifying
x + 13.5 = -18.172781845

Reorder the terms:
13.5 + x = -18.172781845

Solving
13.5 + x = -18.172781845

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = -18.172781845 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = -18.172781845 + -13.5
x = -18.172781845 + -13.5

Combine like terms: -18.172781845 + -13.5 = -31.672781845
x = -31.672781845

Simplifying
x = -31.672781845


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.672781845, -31.672781845}

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