a^2+12a-28=7

Solution for a^2+12a-28=7 equation:

Simplifying
a2 + 12a + -28 = 7

Reorder the terms:
-28 + 12a + a2 = 7

Solving
-28 + 12a + a2 = 7

Solving for variable 'a'.

Reorder the terms:
-28 + -7 + 12a + a2 = 7 + -7

Combine like terms: -28 + -7 = -35
-35 + 12a + a2 = 7 + -7

Combine like terms: 7 + -7 = 0
-35 + 12a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 12a + 35 + a2 = 0 + 35

Reorder the terms:
-35 + 35 + 12a + a2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 12a + a2 = 0 + 35
12a + a2 = 0 + 35

Combine like terms: 0 + 35 = 35
12a + a2 = 35

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 = 35 + 36

Reorder the terms:
36 + 12a + a2 = 35 + 36

Combine like terms: 35 + 36 = 71
36 + 12a + a2 = 71

Factor a perfect square on the left side:
(a + 6)(a + 6) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(a + 6) equal to 8.426149773 and -8.426149773.

Subproblem 1
a + 6 = 8.426149773

Simplifying
a + 6 = 8.426149773

Reorder the terms:
6 + a = 8.426149773

Solving
6 + a = 8.426149773

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 = 8.426149773 + -6

Combine like terms: 6 + -6 = 0
0 + a = 8.426149773 + -6
a = 8.426149773 + -6

Combine like terms: 8.426149773 + -6 = 2.426149773
a = 2.426149773

Simplifying
a = 2.426149773

Subproblem 2
a + 6 = -8.426149773

Simplifying
a + 6 = -8.426149773

Reorder the terms:
6 + a = -8.426149773

Solving
6 + a = -8.426149773

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 = -8.426149773 + -6

Combine like terms: 6 + -6 = 0
0 + a = -8.426149773 + -6
a = -8.426149773 + -6

Combine like terms: -8.426149773 + -6 = -14.426149773
a = -14.426149773

Simplifying
a = -14.426149773

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.426149773, -14.426149773}