12x^2+49x-84=0

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Solution for 12x^2+49x-84=0 equation: 


Simplifying
12x2 + 49x + -84 = 0

Reorder the terms:
-84 + 49x + 12x2 = 0

Solving
-84 + 49x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
-7 + 4.083333333x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 4.083333333x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 4.083333333x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4.083333333x + x2 = 0 + 7
4.083333333x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
4.083333333x + x2 = 7

The x term is 4.083333333x.  Take half its coefficient (2.041666667).
Square it (4.168402779) and add it to both sides.

Add '4.168402779' to each side of the equation.
4.083333333x + 4.168402779 + x2 = 7 + 4.168402779

Reorder the terms:
4.168402779 + 4.083333333x + x2 = 7 + 4.168402779

Combine like terms: 7 + 4.168402779 = 11.168402779
4.168402779 + 4.083333333x + x2 = 11.168402779

Factor a perfect square on the left side:
(x + 2.041666667)(x + 2.041666667) = 11.168402779

Calculate the square root of the right side: 3.341916034

Break this problem into two subproblems by setting 
(x + 2.041666667) equal to 3.341916034 and -3.341916034.


Subproblem 1
x + 2.041666667 = 3.341916034

Simplifying
x + 2.041666667 = 3.341916034

Reorder the terms:
2.041666667 + x = 3.341916034

Solving
2.041666667 + x = 3.341916034

Solving for variable 'x'.

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

Add '-2.041666667' to each side of the equation.
2.041666667 + -2.041666667 + x = 3.341916034 + -2.041666667

Combine like terms: 2.041666667 + -2.041666667 = 0.000000000
0.000000000 + x = 3.341916034 + -2.041666667
x = 3.341916034 + -2.041666667

Combine like terms: 3.341916034 + -2.041666667 = 1.300249367
x = 1.300249367

Simplifying
x = 1.300249367


Subproblem 2
x + 2.041666667 = -3.341916034

Simplifying
x + 2.041666667 = -3.341916034

Reorder the terms:
2.041666667 + x = -3.341916034

Solving
2.041666667 + x = -3.341916034

Solving for variable 'x'.

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

Add '-2.041666667' to each side of the equation.
2.041666667 + -2.041666667 + x = -3.341916034 + -2.041666667

Combine like terms: 2.041666667 + -2.041666667 = 0.000000000
0.000000000 + x = -3.341916034 + -2.041666667
x = -3.341916034 + -2.041666667

Combine like terms: -3.341916034 + -2.041666667 = -5.383582701
x = -5.383582701

Simplifying
x = -5.383582701


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.300249367, -5.383582701}

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