3a^2+5a+40=50

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Solution for 3a^2+5a+40=50 equation: 


Simplifying
3a2 + 5a + 40 = 50

Reorder the terms:
40 + 5a + 3a2 = 50

Solving
40 + 5a + 3a2 = 50

Solving for variable 'a'.

Reorder the terms:
40 + -50 + 5a + 3a2 = 50 + -50

Combine like terms: 40 + -50 = -10
-10 + 5a + 3a2 = 50 + -50

Combine like terms: 50 + -50 = 0
-10 + 5a + 3a2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-3.333333333 + 1.666666667a + a2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 1.666666667a + 3.333333333 + a2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 1.666666667a + a2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 1.666666667a + a2 = 0 + 3.333333333
1.666666667a + a2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
1.666666667a + a2 = 3.333333333

The a term is 1.666666667a.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667a + 0.6944444447 + a2 = 3.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667a + a2 = 3.333333333 + 0.6944444447

Combine like terms: 3.333333333 + 0.6944444447 = 4.0277777777
0.6944444447 + 1.666666667a + a2 = 4.0277777777

Factor a perfect square on the left side:
(a + 0.8333333335)(a + 0.8333333335) = 4.0277777777

Calculate the square root of the right side: 2.00693243

Break this problem into two subproblems by setting 
(a + 0.8333333335) equal to 2.00693243 and -2.00693243.


Subproblem 1
a + 0.8333333335 = 2.00693243

Simplifying
a + 0.8333333335 = 2.00693243

Reorder the terms:
0.8333333335 + a = 2.00693243

Solving
0.8333333335 + a = 2.00693243

Solving for variable 'a'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + a = 2.00693243 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + a = 2.00693243 + -0.8333333335
a = 2.00693243 + -0.8333333335

Combine like terms: 2.00693243 + -0.8333333335 = 1.1735990965
a = 1.1735990965

Simplifying
a = 1.1735990965


Subproblem 2
a + 0.8333333335 = -2.00693243

Simplifying
a + 0.8333333335 = -2.00693243

Reorder the terms:
0.8333333335 + a = -2.00693243

Solving
0.8333333335 + a = -2.00693243

Solving for variable 'a'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + a = -2.00693243 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + a = -2.00693243 + -0.8333333335
a = -2.00693243 + -0.8333333335

Combine like terms: -2.00693243 + -0.8333333335 = -2.8402657635
a = -2.8402657635

Simplifying
a = -2.8402657635


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.1735990965, -2.8402657635}

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