(6x^2)+x-8=0

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Solution for (6x^2)+x-8=0 equation:


Simplifying
(6x2) + x + -8 = 0

Reorder the terms:
-8 + x + (6x2) = 0

Solving
-8 + x + (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'.
-1.333333333 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 0.1666666667x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 0.1666666667x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 0.1666666667x + x2 = 0 + 1.333333333
0.1666666667x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
0.1666666667x + x2 = 1.333333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1666666667x + 0.25 + x2 = 1.333333333 + 0.25

Reorder the terms:
0.25 + 0.1666666667x + x2 = 1.333333333 + 0.25

Combine like terms: 1.333333333 + 0.25 = 1.583333333
0.25 + 0.1666666667x + x2 = 1.583333333

Factor a perfect square on the left side:
((x) + 0.5)((x) + 0.5) = 1.583333333

Calculate the square root of the right side: 1.258305739

Break this problem into two subproblems by setting 
((x) + 0.5) equal to 1.258305739 and -1.258305739.

Subproblem 1

(x) + 0.5 = 1.258305739 Simplifying (x) + 0.5 = 1.258305739 x + 0.5 = 1.258305739 Reorder the terms: 0.5 + x = 1.258305739 Solving 0.5 + x = 1.258305739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.258305739 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.258305739 + -0.5 x = 1.258305739 + -0.5 Combine like terms: 1.258305739 + -0.5 = 0.758305739 x = 0.758305739 Simplifying x = 0.758305739

Subproblem 2

(x) + 0.5 = -1.258305739 Simplifying (x) + 0.5 = -1.258305739 x + 0.5 = -1.258305739 Reorder the terms: 0.5 + x = -1.258305739 Solving 0.5 + x = -1.258305739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.258305739 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.258305739 + -0.5 x = -1.258305739 + -0.5 Combine like terms: -1.258305739 + -0.5 = -1.758305739 x = -1.758305739 Simplifying x = -1.758305739

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.758305739, -1.758305739}

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