3a^2+6a-45=3

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Solution for 3a^2+6a-45=3 equation: 


Simplifying
3a2 + 6a + -45 = 3

Reorder the terms:
-45 + 6a + 3a2 = 3

Solving
-45 + 6a + 3a2 = 3

Solving for variable 'a'.

Reorder the terms:
-45 + -3 + 6a + 3a2 = 3 + -3

Combine like terms: -45 + -3 = -48
-48 + 6a + 3a2 = 3 + -3

Combine like terms: 3 + -3 = 0
-48 + 6a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + 2a + a2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-16 + 2a + a2)' equal to zero and attempt to solve:

Simplifying
-16 + 2a + a2 = 0

Solving
-16 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 2a + 16 + a2 = 0 + 16

Reorder the terms:
-16 + 16 + 2a + a2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 2a + a2 = 0 + 16
2a + a2 = 0 + 16

Combine like terms: 0 + 16 = 16
2a + a2 = 16

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 16 + 1

Reorder the terms:
1 + 2a + a2 = 16 + 1

Combine like terms: 16 + 1 = 17
1 + 2a + a2 = 17

Factor a perfect square on the left side:
(a + 1)(a + 1) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(a + 1) equal to 4.123105626 and -4.123105626.


Subproblem 1
a + 1 = 4.123105626

Simplifying
a + 1 = 4.123105626

Reorder the terms:
1 + a = 4.123105626

Solving
1 + a = 4.123105626

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + a = 4.123105626 + -1

Combine like terms: 1 + -1 = 0
0 + a = 4.123105626 + -1
a = 4.123105626 + -1

Combine like terms: 4.123105626 + -1 = 3.123105626
a = 3.123105626

Simplifying
a = 3.123105626


Subproblem 2
a + 1 = -4.123105626

Simplifying
a + 1 = -4.123105626

Reorder the terms:
1 + a = -4.123105626

Solving
1 + a = -4.123105626

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + a = -4.123105626 + -1

Combine like terms: 1 + -1 = 0
0 + a = -4.123105626 + -1
a = -4.123105626 + -1

Combine like terms: -4.123105626 + -1 = -5.123105626
a = -5.123105626

Simplifying
a = -5.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.123105626, -5.123105626}
Solution
a = {3.123105626, -5.123105626}

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