x^2+12x-2=2

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Solution for x^2+12x-2=2 equation:


Simplifying
x2 + 12x + -2 = 2

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

Solving
-2 + 12x + x2 = 2

Solving for variable 'x'.

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

Combine like terms: -2 + -2 = -4
-4 + 12x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-4 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 12x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 12x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 12x + x2 = 0 + 4
12x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
12x + x2 = 4

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 4 + 36

Reorder the terms:
36 + 12x + x2 = 4 + 36

Combine like terms: 4 + 36 = 40
36 + 12x + x2 = 40

Factor a perfect square on the left side:
(x + 6)(x + 6) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + 6) equal to 6.32455532 and -6.32455532.

Subproblem 1

x + 6 = 6.32455532 Simplifying x + 6 = 6.32455532 Reorder the terms: 6 + x = 6.32455532 Solving 6 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.32455532 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.32455532 + -6 x = 6.32455532 + -6 Combine like terms: 6.32455532 + -6 = 0.32455532 x = 0.32455532 Simplifying x = 0.32455532

Subproblem 2

x + 6 = -6.32455532 Simplifying x + 6 = -6.32455532 Reorder the terms: 6 + x = -6.32455532 Solving 6 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.32455532 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.32455532 + -6 x = -6.32455532 + -6 Combine like terms: -6.32455532 + -6 = -12.32455532 x = -12.32455532 Simplifying x = -12.32455532

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.32455532, -12.32455532}

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