(x+12)(x)=x+2

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Solution for (x+12)(x)=x+2 equation:


Simplifying
(x + 12)(x) = x + 2

Reorder the terms:
(12 + x)(x) = x + 2

Reorder the terms for easier multiplication:
x(12 + x) = x + 2
(12 * x + x * x) = x + 2
(12x + x2) = x + 2

Reorder the terms:
12x + x2 = 2 + x

Solving
12x + x2 = 2 + x

Solving for variable 'x'.

Reorder the terms:
-2 + 12x + -1x + x2 = 2 + x + -2 + -1x

Combine like terms: 12x + -1x = 11x
-2 + 11x + x2 = 2 + x + -2 + -1x

Reorder the terms:
-2 + 11x + x2 = 2 + -2 + x + -1x

Combine like terms: 2 + -2 = 0
-2 + 11x + x2 = 0 + x + -1x
-2 + 11x + x2 = x + -1x

Combine like terms: x + -1x = 0
-2 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 11x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 11x + x2 = 0 + 2

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

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

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 2 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 2 + 30.25

Combine like terms: 2 + 30.25 = 32.25
30.25 + 11x + x2 = 32.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5.678908346 and -5.678908346.

Subproblem 1

x + 5.5 = 5.678908346 Simplifying x + 5.5 = 5.678908346 Reorder the terms: 5.5 + x = 5.678908346 Solving 5.5 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 5.678908346 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.678908346 + -5.5 x = 5.678908346 + -5.5 Combine like terms: 5.678908346 + -5.5 = 0.178908346 x = 0.178908346 Simplifying x = 0.178908346

Subproblem 2

x + 5.5 = -5.678908346 Simplifying x + 5.5 = -5.678908346 Reorder the terms: 5.5 + x = -5.678908346 Solving 5.5 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -5.678908346 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.678908346 + -5.5 x = -5.678908346 + -5.5 Combine like terms: -5.678908346 + -5.5 = -11.178908346 x = -11.178908346 Simplifying x = -11.178908346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.178908346, -11.178908346}

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