x^2+12x=-5

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Solution for x^2+12x=-5 equation:


Simplifying
x2 + 12x = -5

Reorder the terms:
12x + x2 = -5

Solving
12x + x2 = -5

Solving for variable 'x'.

Reorder the terms:
5 + 12x + x2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 12x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 12x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 12x + x2 = 0 + -5
12x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
12x + x2 = -5

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 = -5 + 36

Reorder the terms:
36 + 12x + x2 = -5 + 36

Combine like terms: -5 + 36 = 31
36 + 12x + x2 = 31

Factor a perfect square on the left side:
(x + 6)(x + 6) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + 6) equal to 5.567764363 and -5.567764363.

Subproblem 1

x + 6 = 5.567764363 Simplifying x + 6 = 5.567764363 Reorder the terms: 6 + x = 5.567764363 Solving 6 + x = 5.567764363 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 = 5.567764363 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.567764363 + -6 x = 5.567764363 + -6 Combine like terms: 5.567764363 + -6 = -0.432235637 x = -0.432235637 Simplifying x = -0.432235637

Subproblem 2

x + 6 = -5.567764363 Simplifying x + 6 = -5.567764363 Reorder the terms: 6 + x = -5.567764363 Solving 6 + x = -5.567764363 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 = -5.567764363 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.567764363 + -6 x = -5.567764363 + -6 Combine like terms: -5.567764363 + -6 = -11.567764363 x = -11.567764363 Simplifying x = -11.567764363

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.432235637, -11.567764363}

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