x^2-2x-12x-47=0

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Solution for x^2-2x-12x-47=0 equation: 


Simplifying
x2 + -2x + -12x + -47 = 0

Reorder the terms:
-47 + -2x + -12x + x2 = 0

Combine like terms: -2x + -12x = -14x
-47 + -14x + x2 = 0

Solving
-47 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -14x + 47 + x2 = 0 + 47

Reorder the terms:
-47 + 47 + -14x + x2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -14x + x2 = 0 + 47
-14x + x2 = 0 + 47

Combine like terms: 0 + 47 = 47
-14x + x2 = 47

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 = 47 + 49

Reorder the terms:
49 + -14x + x2 = 47 + 49

Combine like terms: 47 + 49 = 96
49 + -14x + x2 = 96

Factor a perfect square on the left side:
(x + -7)(x + -7) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(x + -7) equal to 9.797958971 and -9.797958971.


Subproblem 1
x + -7 = 9.797958971

Simplifying
x + -7 = 9.797958971

Reorder the terms:
-7 + x = 9.797958971

Solving
-7 + x = 9.797958971

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 = 9.797958971 + 7

Combine like terms: -7 + 7 = 0
0 + x = 9.797958971 + 7
x = 9.797958971 + 7

Combine like terms: 9.797958971 + 7 = 16.797958971
x = 16.797958971

Simplifying
x = 16.797958971


Subproblem 2
x + -7 = -9.797958971

Simplifying
x + -7 = -9.797958971

Reorder the terms:
-7 + x = -9.797958971

Solving
-7 + x = -9.797958971

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 = -9.797958971 + 7

Combine like terms: -7 + 7 = 0
0 + x = -9.797958971 + 7
x = -9.797958971 + 7

Combine like terms: -9.797958971 + 7 = -2.797958971
x = -2.797958971

Simplifying
x = -2.797958971


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.797958971, -2.797958971}

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