(2x*x)-x-8=0

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Solution for (2x*x)-x-8=0 equation:


Simplifying
(2x * x) + -1x + -8 = 0

Multiply x * x
(2x2) + -1x + -8 = 0

Reorder the terms:
-8 + -1x + (2x2) = 0

Solving
-8 + -1x + (2x2) = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-4 + -0.5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -0.5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -0.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -0.5x + x2 = 0 + 4
-0.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-0.5x + x2 = 4

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 4 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 4 + 0.0625

Combine like terms: 4 + 0.0625 = 4.0625
0.0625 + -0.5x + x2 = 4.0625

Factor a perfect square on the left side:
((x) + -0.25)((x) + -0.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
((x) + -0.25) equal to 2.015564437 and -2.015564437.

Subproblem 1

(x) + -0.25 = 2.015564437 Simplifying (x) + -0.25 = 2.015564437 x + -0.25 = 2.015564437 Reorder the terms: -0.25 + x = 2.015564437 Solving -0.25 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.015564437 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.015564437 + 0.25 x = 2.015564437 + 0.25 Combine like terms: 2.015564437 + 0.25 = 2.265564437 x = 2.265564437 Simplifying x = 2.265564437

Subproblem 2

(x) + -0.25 = -2.015564437 Simplifying (x) + -0.25 = -2.015564437 x + -0.25 = -2.015564437 Reorder the terms: -0.25 + x = -2.015564437 Solving -0.25 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.015564437 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.015564437 + 0.25 x = -2.015564437 + 0.25 Combine like terms: -2.015564437 + 0.25 = -1.765564437 x = -1.765564437 Simplifying x = -1.765564437

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.265564437, -1.765564437}

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