a^2+12a-36=0

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Solution for a^2+12a-36=0 equation:


Simplifying
a2 + 12a + -36 = 0

Reorder the terms:
-36 + 12a + a2 = 0

Solving
-36 + 12a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 12a + 36 + a2 = 0 + 36

Reorder the terms:
-36 + 36 + 12a + a2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 12a + a2 = 0 + 36
12a + a2 = 0 + 36

Combine like terms: 0 + 36 = 36
12a + a2 = 36

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 = 36 + 36

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

Combine like terms: 36 + 36 = 72
36 + 12a + a2 = 72

Factor a perfect square on the left side:
(a + 6)(a + 6) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(a + 6) equal to 8.485281374 and -8.485281374.

Subproblem 1

a + 6 = 8.485281374 Simplifying a + 6 = 8.485281374 Reorder the terms: 6 + a = 8.485281374 Solving 6 + a = 8.485281374 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 = 8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + a = 8.485281374 + -6 a = 8.485281374 + -6 Combine like terms: 8.485281374 + -6 = 2.485281374 a = 2.485281374 Simplifying a = 2.485281374

Subproblem 2

a + 6 = -8.485281374 Simplifying a + 6 = -8.485281374 Reorder the terms: 6 + a = -8.485281374 Solving 6 + a = -8.485281374 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 = -8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + a = -8.485281374 + -6 a = -8.485281374 + -6 Combine like terms: -8.485281374 + -6 = -14.485281374 a = -14.485281374 Simplifying a = -14.485281374

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.485281374, -14.485281374}

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