a^2+12a+13=0

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Solution for a^2+12a+13=0 equation:


Simplifying
a2 + 12a + 13 = 0

Reorder the terms:
13 + 12a + a2 = 0

Solving
13 + 12a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 12a + -13 + a2 = 0 + -13

Reorder the terms:
13 + -13 + 12a + a2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 12a + a2 = 0 + -13
12a + a2 = 0 + -13

Combine like terms: 0 + -13 = -13
12a + a2 = -13

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

Add '36' to each side of the equation.
12a + 36 + a2 = -13 + 36

Reorder the terms:
36 + 12a + a2 = -13 + 36

Combine like terms: -13 + 36 = 23
36 + 12a + a2 = 23

Factor a perfect square on the left side:
(a + 6)(a + 6) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(a + 6) equal to 4.795831523 and -4.795831523.

Subproblem 1

a + 6 = 4.795831523 Simplifying a + 6 = 4.795831523 Reorder the terms: 6 + a = 4.795831523 Solving 6 + a = 4.795831523 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = 4.795831523 + -6 Combine like terms: 6 + -6 = 0 0 + a = 4.795831523 + -6 a = 4.795831523 + -6 Combine like terms: 4.795831523 + -6 = -1.204168477 a = -1.204168477 Simplifying a = -1.204168477

Subproblem 2

a + 6 = -4.795831523 Simplifying a + 6 = -4.795831523 Reorder the terms: 6 + a = -4.795831523 Solving 6 + a = -4.795831523 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = -4.795831523 + -6 Combine like terms: 6 + -6 = 0 0 + a = -4.795831523 + -6 a = -4.795831523 + -6 Combine like terms: -4.795831523 + -6 = -10.795831523 a = -10.795831523 Simplifying a = -10.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-1.204168477, -10.795831523}

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