2x^2-96=x

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Solution for 2x^2-96=x equation:


Simplifying
2x2 + -96 = x

Reorder the terms:
-96 + 2x2 = x

Solving
-96 + 2x2 = x

Solving for variable 'x'.

Reorder the terms:
-96 + -1x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-96 + -1x + 2x2 = 0

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

Divide each side by '2'.
-48 + -0.5x + x2 = 0

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + -0.5x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + -0.5x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -0.5x + x2 = 0 + 48
-0.5x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
-0.5x + x2 = 48

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 = 48 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 48 + 0.0625

Combine like terms: 48 + 0.0625 = 48.0625
0.0625 + -0.5x + x2 = 48.0625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 48.0625

Calculate the square root of the right side: 6.932712312

Break this problem into two subproblems by setting 
(x + -0.25) equal to 6.932712312 and -6.932712312.

Subproblem 1

x + -0.25 = 6.932712312 Simplifying x + -0.25 = 6.932712312 Reorder the terms: -0.25 + x = 6.932712312 Solving -0.25 + x = 6.932712312 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 = 6.932712312 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 6.932712312 + 0.25 x = 6.932712312 + 0.25 Combine like terms: 6.932712312 + 0.25 = 7.182712312 x = 7.182712312 Simplifying x = 7.182712312

Subproblem 2

x + -0.25 = -6.932712312 Simplifying x + -0.25 = -6.932712312 Reorder the terms: -0.25 + x = -6.932712312 Solving -0.25 + x = -6.932712312 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 = -6.932712312 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -6.932712312 + 0.25 x = -6.932712312 + 0.25 Combine like terms: -6.932712312 + 0.25 = -6.682712312 x = -6.682712312 Simplifying x = -6.682712312

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.182712312, -6.682712312}

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