(x+4)*x=262

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Solution for (x+4)*x=262 equation: 


Simplifying
(x + 4) * x = 262

Reorder the terms:
(4 + x) * x = 262

Reorder the terms for easier multiplication:
x(4 + x) = 262
(4 * x + x * x) = 262
(4x + x2) = 262

Solving
4x + x2 = 262

Solving for variable 'x'.

Reorder the terms:
-262 + 4x + x2 = 262 + -262

Combine like terms: 262 + -262 = 0
-262 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '262' to each side of the equation.
-262 + 4x + 262 + x2 = 0 + 262

Reorder the terms:
-262 + 262 + 4x + x2 = 0 + 262

Combine like terms: -262 + 262 = 0
0 + 4x + x2 = 0 + 262
4x + x2 = 0 + 262

Combine like terms: 0 + 262 = 262
4x + x2 = 262

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 262 + 4

Reorder the terms:
4 + 4x + x2 = 262 + 4

Combine like terms: 262 + 4 = 266
4 + 4x + x2 = 266

Factor a perfect square on the left side:
(x + 2)(x + 2) = 266

Calculate the square root of the right side: 16.30950643

Break this problem into two subproblems by setting 
(x + 2) equal to 16.30950643 and -16.30950643.


Subproblem 1
x + 2 = 16.30950643

Simplifying
x + 2 = 16.30950643

Reorder the terms:
2 + x = 16.30950643

Solving
2 + x = 16.30950643

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 16.30950643 + -2

Combine like terms: 2 + -2 = 0
0 + x = 16.30950643 + -2
x = 16.30950643 + -2

Combine like terms: 16.30950643 + -2 = 14.30950643
x = 14.30950643

Simplifying
x = 14.30950643


Subproblem 2
x + 2 = -16.30950643

Simplifying
x + 2 = -16.30950643

Reorder the terms:
2 + x = -16.30950643

Solving
2 + x = -16.30950643

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -16.30950643 + -2

Combine like terms: 2 + -2 = 0
0 + x = -16.30950643 + -2
x = -16.30950643 + -2

Combine like terms: -16.30950643 + -2 = -18.30950643
x = -18.30950643

Simplifying
x = -18.30950643


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.30950643, -18.30950643}

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