x(14+x)=255

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Solution for x(14+x)=255 equation:


Simplifying
x(14 + x) = 255
(14 * x + x * x) = 255
(14x + x2) = 255

Solving
14x + x2 = 255

Solving for variable 'x'.

Reorder the terms:
-255 + 14x + x2 = 255 + -255

Combine like terms: 255 + -255 = 0
-255 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '255' to each side of the equation.
-255 + 14x + 255 + x2 = 0 + 255

Reorder the terms:
-255 + 255 + 14x + x2 = 0 + 255

Combine like terms: -255 + 255 = 0
0 + 14x + x2 = 0 + 255
14x + x2 = 0 + 255

Combine like terms: 0 + 255 = 255
14x + x2 = 255

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 255 + 49

Reorder the terms:
49 + 14x + x2 = 255 + 49

Combine like terms: 255 + 49 = 304
49 + 14x + x2 = 304

Factor a perfect square on the left side:
(x + 7)(x + 7) = 304

Calculate the square root of the right side: 17.435595774

Break this problem into two subproblems by setting 
(x + 7) equal to 17.435595774 and -17.435595774.


Subproblem 1
x + 7 = 17.435595774

Simplifying
x + 7 = 17.435595774

Reorder the terms:
7 + x = 17.435595774

Solving
7 + x = 17.435595774

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 17.435595774 + -7

Combine like terms: 7 + -7 = 0
0 + x = 17.435595774 + -7
x = 17.435595774 + -7

Combine like terms: 17.435595774 + -7 = 10.435595774
x = 10.435595774

Simplifying
x = 10.435595774


Subproblem 2
x + 7 = -17.435595774

Simplifying
x + 7 = -17.435595774

Reorder the terms:
7 + x = -17.435595774

Solving
7 + x = -17.435595774

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -17.435595774 + -7

Combine like terms: 7 + -7 = 0
0 + x = -17.435595774 + -7
x = -17.435595774 + -7

Combine like terms: -17.435595774 + -7 = -24.435595774
x = -24.435595774

Simplifying
x = -24.435595774


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.435595774, -24.435595774}

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