6x^2-14x-49=0

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Solution for 6x^2-14x-49=0 equation: 


Simplifying
6x2 + -14x + -49 = 0

Reorder the terms:
-49 + -14x + 6x2 = 0

Solving
-49 + -14x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-8.166666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '8.166666667' to each side of the equation.
-8.166666667 + -2.333333333x + 8.166666667 + x2 = 0 + 8.166666667

Reorder the terms:
-8.166666667 + 8.166666667 + -2.333333333x + x2 = 0 + 8.166666667

Combine like terms: -8.166666667 + 8.166666667 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + 8.166666667
-2.333333333x + x2 = 0 + 8.166666667

Combine like terms: 0 + 8.166666667 = 8.166666667
-2.333333333x + x2 = 8.166666667

The x term is -2.333333333x.  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.
-2.333333333x + 1.361111112 + x2 = 8.166666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 8.166666667 + 1.361111112

Combine like terms: 8.166666667 + 1.361111112 = 9.527777779
1.361111112 + -2.333333333x + x2 = 9.527777779

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 9.527777779

Calculate the square root of the right side: 3.086709863

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 3.086709863 and -3.086709863.


Subproblem 1
x + -1.166666667 = 3.086709863

Simplifying
x + -1.166666667 = 3.086709863

Reorder the terms:
-1.166666667 + x = 3.086709863

Solving
-1.166666667 + x = 3.086709863

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 3.086709863 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 3.086709863 + 1.166666667
x = 3.086709863 + 1.166666667

Combine like terms: 3.086709863 + 1.166666667 = 4.25337653
x = 4.25337653

Simplifying
x = 4.25337653


Subproblem 2
x + -1.166666667 = -3.086709863

Simplifying
x + -1.166666667 = -3.086709863

Reorder the terms:
-1.166666667 + x = -3.086709863

Solving
-1.166666667 + x = -3.086709863

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -3.086709863 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -3.086709863 + 1.166666667
x = -3.086709863 + 1.166666667

Combine like terms: -3.086709863 + 1.166666667 = -1.920043196
x = -1.920043196

Simplifying
x = -1.920043196


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.25337653, -1.920043196}

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