6x^2+14x-7=0

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Solution for 6x^2+14x-7=0 equation: 


Simplifying
6x2 + 14x + -7 = 0

Reorder the terms:
-7 + 14x + 6x2 = 0

Solving
-7 + 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'.
-1.166666667 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 2.333333333x + 1.166666667 + x2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 2.333333333x + x2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + 1.166666667
2.333333333x + x2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
2.333333333x + x2 = 1.166666667

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 = 1.166666667 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 1.166666667 + 1.361111112

Combine like terms: 1.166666667 + 1.361111112 = 2.527777779
1.361111112 + 2.333333333x + x2 = 2.527777779

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 2.527777779

Calculate the square root of the right side: 1.589898669

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 1.589898669 and -1.589898669.


Subproblem 1
x + 1.166666667 = 1.589898669

Simplifying
x + 1.166666667 = 1.589898669

Reorder the terms:
1.166666667 + x = 1.589898669

Solving
1.166666667 + x = 1.589898669

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 = 1.589898669 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 1.589898669 + -1.166666667
x = 1.589898669 + -1.166666667

Combine like terms: 1.589898669 + -1.166666667 = 0.423232002
x = 0.423232002

Simplifying
x = 0.423232002


Subproblem 2
x + 1.166666667 = -1.589898669

Simplifying
x + 1.166666667 = -1.589898669

Reorder the terms:
1.166666667 + x = -1.589898669

Solving
1.166666667 + x = -1.589898669

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 = -1.589898669 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -1.589898669 + -1.166666667
x = -1.589898669 + -1.166666667

Combine like terms: -1.589898669 + -1.166666667 = -2.756565336
x = -2.756565336

Simplifying
x = -2.756565336


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.423232002, -2.756565336}

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