a^2+6a+9=27

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Solution for a^2+6a+9=27 equation:


Simplifying
a2 + 6a + 9 = 27

Reorder the terms:
9 + 6a + a2 = 27

Solving
9 + 6a + a2 = 27

Solving for variable 'a'.

Reorder the terms:
9 + -27 + 6a + a2 = 27 + -27

Combine like terms: 9 + -27 = -18
-18 + 6a + a2 = 27 + -27

Combine like terms: 27 + -27 = 0
-18 + 6a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 6a + 18 + a2 = 0 + 18

Reorder the terms:
-18 + 18 + 6a + a2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 6a + a2 = 0 + 18
6a + a2 = 0 + 18

Combine like terms: 0 + 18 = 18
6a + a2 = 18

The a term is 6a.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6a + 9 + a2 = 18 + 9

Reorder the terms:
9 + 6a + a2 = 18 + 9

Combine like terms: 18 + 9 = 27
9 + 6a + a2 = 27

Factor a perfect square on the left side:
(a + 3)(a + 3) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(a + 3) equal to 5.196152423 and -5.196152423.

Subproblem 1

a + 3 = 5.196152423 Simplifying a + 3 = 5.196152423 Reorder the terms: 3 + a = 5.196152423 Solving 3 + a = 5.196152423 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 5.196152423 + -3 Combine like terms: 3 + -3 = 0 0 + a = 5.196152423 + -3 a = 5.196152423 + -3 Combine like terms: 5.196152423 + -3 = 2.196152423 a = 2.196152423 Simplifying a = 2.196152423

Subproblem 2

a + 3 = -5.196152423 Simplifying a + 3 = -5.196152423 Reorder the terms: 3 + a = -5.196152423 Solving 3 + a = -5.196152423 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -5.196152423 + -3 Combine like terms: 3 + -3 = 0 0 + a = -5.196152423 + -3 a = -5.196152423 + -3 Combine like terms: -5.196152423 + -3 = -8.196152423 a = -8.196152423 Simplifying a = -8.196152423

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.196152423, -8.196152423}

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