=6x^2-14x-5

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Solution for =6x^2-14x-5 equation:


Simplifying
0 = 6x2 + -14x + -5

Reorder the terms:
0 = -5 + -14x + 6x2

Solving
0 = -5 + -14x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 5 = 5
5 + 14x + -6x2 = -5 + -14x + 6x2 + 5 + 14x + -6x2

Reorder the terms:
5 + 14x + -6x2 = -5 + 5 + -14x + 14x + 6x2 + -6x2

Combine like terms: -5 + 5 = 0
5 + 14x + -6x2 = 0 + -14x + 14x + 6x2 + -6x2
5 + 14x + -6x2 = -14x + 14x + 6x2 + -6x2

Combine like terms: -14x + 14x = 0
5 + 14x + -6x2 = 0 + 6x2 + -6x2
5 + 14x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
5 + 14x + -6x2 = 0

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

Divide each side by '-6'.
-0.8333333333 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -2.333333333x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -2.333333333x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -2.333333333x + x2 = 0 + 0.8333333333
-2.333333333x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-2.333333333x + x2 = 0.8333333333

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 = 0.8333333333 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 0.8333333333 + 1.361111112

Combine like terms: 0.8333333333 + 1.361111112 = 2.1944444453
1.361111112 + -2.333333333x + x2 = 2.1944444453

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 2.1944444453

Calculate the square root of the right side: 1.481365737

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 1.481365737 and -1.481365737.

Subproblem 1

x + -1.166666667 = 1.481365737 Simplifying x + -1.166666667 = 1.481365737 Reorder the terms: -1.166666667 + x = 1.481365737 Solving -1.166666667 + x = 1.481365737 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 = 1.481365737 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.481365737 + 1.166666667 x = 1.481365737 + 1.166666667 Combine like terms: 1.481365737 + 1.166666667 = 2.648032404 x = 2.648032404 Simplifying x = 2.648032404

Subproblem 2

x + -1.166666667 = -1.481365737 Simplifying x + -1.166666667 = -1.481365737 Reorder the terms: -1.166666667 + x = -1.481365737 Solving -1.166666667 + x = -1.481365737 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 = -1.481365737 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.481365737 + 1.166666667 x = -1.481365737 + 1.166666667 Combine like terms: -1.481365737 + 1.166666667 = -0.31469907 x = -0.31469907 Simplifying x = -0.31469907

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.648032404, -0.31469907}

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