2x^2-x-112=0

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Solution for 2x^2-x-112=0 equation:


Simplifying
2x2 + -1x + -112 = 0

Reorder the terms:
-112 + -1x + 2x2 = 0

Solving
-112 + -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'.
-56 + -0.5x + x2 = 0

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + -0.5x + 56 + x2 = 0 + 56

Reorder the terms:
-56 + 56 + -0.5x + x2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + -0.5x + x2 = 0 + 56
-0.5x + x2 = 0 + 56

Combine like terms: 0 + 56 = 56
-0.5x + x2 = 56

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 = 56 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 56 + 0.0625

Combine like terms: 56 + 0.0625 = 56.0625
0.0625 + -0.5x + x2 = 56.0625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 56.0625

Calculate the square root of the right side: 7.487489566

Break this problem into two subproblems by setting 
(x + -0.25) equal to 7.487489566 and -7.487489566.

Subproblem 1

x + -0.25 = 7.487489566 Simplifying x + -0.25 = 7.487489566 Reorder the terms: -0.25 + x = 7.487489566 Solving -0.25 + x = 7.487489566 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 = 7.487489566 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 7.487489566 + 0.25 x = 7.487489566 + 0.25 Combine like terms: 7.487489566 + 0.25 = 7.737489566 x = 7.737489566 Simplifying x = 7.737489566

Subproblem 2

x + -0.25 = -7.487489566 Simplifying x + -0.25 = -7.487489566 Reorder the terms: -0.25 + x = -7.487489566 Solving -0.25 + x = -7.487489566 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 = -7.487489566 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -7.487489566 + 0.25 x = -7.487489566 + 0.25 Combine like terms: -7.487489566 + 0.25 = -7.237489566 x = -7.237489566 Simplifying x = -7.237489566

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.737489566, -7.237489566}

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