6x^2-x-3=0

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Solution for 6x^2-x-3=0 equation:


Simplifying
6x2 + -1x + -3 = 0

Reorder the terms:
-3 + -1x + 6x2 = 0

Solving
-3 + -1x + 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'.
-0.5 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.1666666667x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.1666666667x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.1666666667x + x2 = 0 + 0.5
-0.1666666667x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.1666666667x + x2 = 0.5

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = 0.5 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 0.5 + 0.006944444447

Combine like terms: 0.5 + 0.006944444447 = 0.506944444447
0.006944444447 + -0.1666666667x + x2 = 0.506944444447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 0.506944444447

Calculate the square root of the right side: 0.712000312

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 0.712000312 and -0.712000312.

Subproblem 1

x + -0.08333333335 = 0.712000312 Simplifying x + -0.08333333335 = 0.712000312 Reorder the terms: -0.08333333335 + x = 0.712000312 Solving -0.08333333335 + x = 0.712000312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 0.712000312 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 0.712000312 + 0.08333333335 x = 0.712000312 + 0.08333333335 Combine like terms: 0.712000312 + 0.08333333335 = 0.79533364535 x = 0.79533364535 Simplifying x = 0.79533364535

Subproblem 2

x + -0.08333333335 = -0.712000312 Simplifying x + -0.08333333335 = -0.712000312 Reorder the terms: -0.08333333335 + x = -0.712000312 Solving -0.08333333335 + x = -0.712000312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -0.712000312 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -0.712000312 + 0.08333333335 x = -0.712000312 + 0.08333333335 Combine like terms: -0.712000312 + 0.08333333335 = -0.62866697865 x = -0.62866697865 Simplifying x = -0.62866697865

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.79533364535, -0.62866697865}

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