3a^2+7a-49=0

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Solution for 3a^2+7a-49=0 equation: 


Simplifying
3a2 + 7a + -49 = 0

Reorder the terms:
-49 + 7a + 3a2 = 0

Solving
-49 + 7a + 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'.
-16.33333333 + 2.333333333a + a2 = 0

Move the constant term to the right:

Add '16.33333333' to each side of the equation.
-16.33333333 + 2.333333333a + 16.33333333 + a2 = 0 + 16.33333333

Reorder the terms:
-16.33333333 + 16.33333333 + 2.333333333a + a2 = 0 + 16.33333333

Combine like terms: -16.33333333 + 16.33333333 = 0.00000000
0.00000000 + 2.333333333a + a2 = 0 + 16.33333333
2.333333333a + a2 = 0 + 16.33333333

Combine like terms: 0 + 16.33333333 = 16.33333333
2.333333333a + a2 = 16.33333333

The a term is 2.333333333a.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333a + 1.361111112 + a2 = 16.33333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333a + a2 = 16.33333333 + 1.361111112

Combine like terms: 16.33333333 + 1.361111112 = 17.694444442
1.361111112 + 2.333333333a + a2 = 17.694444442

Factor a perfect square on the left side:
(a + 1.166666667)(a + 1.166666667) = 17.694444442

Calculate the square root of the right side: 4.206476488

Break this problem into two subproblems by setting 
(a + 1.166666667) equal to 4.206476488 and -4.206476488.


Subproblem 1
a + 1.166666667 = 4.206476488

Simplifying
a + 1.166666667 = 4.206476488

Reorder the terms:
1.166666667 + a = 4.206476488

Solving
1.166666667 + a = 4.206476488

Solving for variable 'a'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + a = 4.206476488 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + a = 4.206476488 + -1.166666667
a = 4.206476488 + -1.166666667

Combine like terms: 4.206476488 + -1.166666667 = 3.039809821
a = 3.039809821

Simplifying
a = 3.039809821


Subproblem 2
a + 1.166666667 = -4.206476488

Simplifying
a + 1.166666667 = -4.206476488

Reorder the terms:
1.166666667 + a = -4.206476488

Solving
1.166666667 + a = -4.206476488

Solving for variable 'a'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + a = -4.206476488 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + a = -4.206476488 + -1.166666667
a = -4.206476488 + -1.166666667

Combine like terms: -4.206476488 + -1.166666667 = -5.373143155
a = -5.373143155

Simplifying
a = -5.373143155


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.039809821, -5.373143155}

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