12x^2+49x-51=0

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Solution for 12x^2+49x-51=0 equation: 


Simplifying
12x2 + 49x + -51 = 0

Reorder the terms:
-51 + 49x + 12x2 = 0

Solving
-51 + 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'.
-4.25 + 4.083333333x + x2 = 0

Move the constant term to the right:

Add '4.25' to each side of the equation.
-4.25 + 4.083333333x + 4.25 + x2 = 0 + 4.25

Reorder the terms:
-4.25 + 4.25 + 4.083333333x + x2 = 0 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + 4.083333333x + x2 = 0 + 4.25
4.083333333x + x2 = 0 + 4.25

Combine like terms: 0 + 4.25 = 4.25
4.083333333x + x2 = 4.25

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 = 4.25 + 4.168402779

Reorder the terms:
4.168402779 + 4.083333333x + x2 = 4.25 + 4.168402779

Combine like terms: 4.25 + 4.168402779 = 8.418402779
4.168402779 + 4.083333333x + x2 = 8.418402779

Factor a perfect square on the left side:
(x + 2.041666667)(x + 2.041666667) = 8.418402779

Calculate the square root of the right side: 2.901448393

Break this problem into two subproblems by setting 
(x + 2.041666667) equal to 2.901448393 and -2.901448393.


Subproblem 1
x + 2.041666667 = 2.901448393

Simplifying
x + 2.041666667 = 2.901448393

Reorder the terms:
2.041666667 + x = 2.901448393

Solving
2.041666667 + x = 2.901448393

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 = 2.901448393 + -2.041666667

Combine like terms: 2.041666667 + -2.041666667 = 0.000000000
0.000000000 + x = 2.901448393 + -2.041666667
x = 2.901448393 + -2.041666667

Combine like terms: 2.901448393 + -2.041666667 = 0.859781726
x = 0.859781726

Simplifying
x = 0.859781726


Subproblem 2
x + 2.041666667 = -2.901448393

Simplifying
x + 2.041666667 = -2.901448393

Reorder the terms:
2.041666667 + x = -2.901448393

Solving
2.041666667 + x = -2.901448393

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 = -2.901448393 + -2.041666667

Combine like terms: 2.041666667 + -2.041666667 = 0.000000000
0.000000000 + x = -2.901448393 + -2.041666667
x = -2.901448393 + -2.041666667

Combine like terms: -2.901448393 + -2.041666667 = -4.94311506
x = -4.94311506

Simplifying
x = -4.94311506


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.859781726, -4.94311506}

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