3a^2+5a-242=0

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Solution for 3a^2+5a-242=0 equation:


Simplifying
3a2 + 5a + -242 = 0

Reorder the terms:
-242 + 5a + 3a2 = 0

Solving
-242 + 5a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
-80.66666667 + 1.666666667a + a2 = 0

Move the constant term to the right:

Add '80.66666667' to each side of the equation.
-80.66666667 + 1.666666667a + 80.66666667 + a2 = 0 + 80.66666667

Reorder the terms:
-80.66666667 + 80.66666667 + 1.666666667a + a2 = 0 + 80.66666667

Combine like terms: -80.66666667 + 80.66666667 = 0.00000000
0.00000000 + 1.666666667a + a2 = 0 + 80.66666667
1.666666667a + a2 = 0 + 80.66666667

Combine like terms: 0 + 80.66666667 = 80.66666667
1.666666667a + a2 = 80.66666667

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 = 80.66666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667a + a2 = 80.66666667 + 0.6944444447

Combine like terms: 80.66666667 + 0.6944444447 = 81.3611111147
0.6944444447 + 1.666666667a + a2 = 81.3611111147

Factor a perfect square on the left side:
(a + 0.8333333335)(a + 0.8333333335) = 81.3611111147

Calculate the square root of the right side: 9.020039419

Break this problem into two subproblems by setting 
(a + 0.8333333335) equal to 9.020039419 and -9.020039419.


Subproblem 1
a + 0.8333333335 = 9.020039419

Simplifying
a + 0.8333333335 = 9.020039419

Reorder the terms:
0.8333333335 + a = 9.020039419

Solving
0.8333333335 + a = 9.020039419

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 = 9.020039419 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + a = 9.020039419 + -0.8333333335
a = 9.020039419 + -0.8333333335

Combine like terms: 9.020039419 + -0.8333333335 = 8.1867060855
a = 8.1867060855

Simplifying
a = 8.1867060855


Subproblem 2
a + 0.8333333335 = -9.020039419

Simplifying
a + 0.8333333335 = -9.020039419

Reorder the terms:
0.8333333335 + a = -9.020039419

Solving
0.8333333335 + a = -9.020039419

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 = -9.020039419 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + a = -9.020039419 + -0.8333333335
a = -9.020039419 + -0.8333333335

Combine like terms: -9.020039419 + -0.8333333335 = -9.8533727525
a = -9.8533727525

Simplifying
a = -9.8533727525


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {8.1867060855, -9.8533727525}

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