a^2+3a-44=0

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Solution for a^2+3a-44=0 equation: 


Simplifying
a2 + 3a + -44 = 0

Reorder the terms:
-44 + 3a + a2 = 0

Solving
-44 + 3a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + 3a + 44 + a2 = 0 + 44

Reorder the terms:
-44 + 44 + 3a + a2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + 3a + a2 = 0 + 44
3a + a2 = 0 + 44

Combine like terms: 0 + 44 = 44
3a + a2 = 44

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = 44 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 44 + 2.25

Combine like terms: 44 + 2.25 = 46.25
2.25 + 3a + a2 = 46.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(a + 1.5) equal to 6.800735254 and -6.800735254.


Subproblem 1
a + 1.5 = 6.800735254

Simplifying
a + 1.5 = 6.800735254

Reorder the terms:
1.5 + a = 6.800735254

Solving
1.5 + a = 6.800735254

Solving for variable 'a'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = 6.800735254 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = 6.800735254 + -1.5
a = 6.800735254 + -1.5

Combine like terms: 6.800735254 + -1.5 = 5.300735254
a = 5.300735254

Simplifying
a = 5.300735254


Subproblem 2
a + 1.5 = -6.800735254

Simplifying
a + 1.5 = -6.800735254

Reorder the terms:
1.5 + a = -6.800735254

Solving
1.5 + a = -6.800735254

Solving for variable 'a'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = -6.800735254 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = -6.800735254 + -1.5
a = -6.800735254 + -1.5

Combine like terms: -6.800735254 + -1.5 = -8.300735254
a = -8.300735254

Simplifying
a = -8.300735254


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {5.300735254, -8.300735254}

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