x^2+12x=-10

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Solution for x^2+12x=-10 equation:


Simplifying
x2 + 12x = -10

Reorder the terms:
12x + x2 = -10

Solving
12x + x2 = -10

Solving for variable 'x'.

Reorder the terms:
10 + 12x + x2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 12x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 12x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 12x + x2 = 0 + -10
12x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
12x + x2 = -10

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 = -10 + 36

Reorder the terms:
36 + 12x + x2 = -10 + 36

Combine like terms: -10 + 36 = 26
36 + 12x + x2 = 26

Factor a perfect square on the left side:
(x + 6)(x + 6) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + 6) equal to 5.099019514 and -5.099019514.

Subproblem 1

x + 6 = 5.099019514 Simplifying x + 6 = 5.099019514 Reorder the terms: 6 + x = 5.099019514 Solving 6 + x = 5.099019514 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 = 5.099019514 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.099019514 + -6 x = 5.099019514 + -6 Combine like terms: 5.099019514 + -6 = -0.900980486 x = -0.900980486 Simplifying x = -0.900980486

Subproblem 2

x + 6 = -5.099019514 Simplifying x + 6 = -5.099019514 Reorder the terms: 6 + x = -5.099019514 Solving 6 + x = -5.099019514 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 = -5.099019514 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.099019514 + -6 x = -5.099019514 + -6 Combine like terms: -5.099019514 + -6 = -11.099019514 x = -11.099019514 Simplifying x = -11.099019514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.900980486, -11.099019514}

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