2x^2-x-185=0

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Solution for 2x^2-x-185=0 equation:


Simplifying
2x2 + -1x + -185 = 0

Reorder the terms:
-185 + -1x + 2x2 = 0

Solving
-185 + -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'.
-92.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '92.5' to each side of the equation.
-92.5 + -0.5x + 92.5 + x2 = 0 + 92.5

Reorder the terms:
-92.5 + 92.5 + -0.5x + x2 = 0 + 92.5

Combine like terms: -92.5 + 92.5 = 0.0
0.0 + -0.5x + x2 = 0 + 92.5
-0.5x + x2 = 0 + 92.5

Combine like terms: 0 + 92.5 = 92.5
-0.5x + x2 = 92.5

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 = 92.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 92.5 + 0.0625

Combine like terms: 92.5 + 0.0625 = 92.5625
0.0625 + -0.5x + x2 = 92.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 92.5625

Calculate the square root of the right side: 9.620940702

Break this problem into two subproblems by setting 
(x + -0.25) equal to 9.620940702 and -9.620940702.

Subproblem 1

x + -0.25 = 9.620940702 Simplifying x + -0.25 = 9.620940702 Reorder the terms: -0.25 + x = 9.620940702 Solving -0.25 + x = 9.620940702 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 = 9.620940702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 9.620940702 + 0.25 x = 9.620940702 + 0.25 Combine like terms: 9.620940702 + 0.25 = 9.870940702 x = 9.870940702 Simplifying x = 9.870940702

Subproblem 2

x + -0.25 = -9.620940702 Simplifying x + -0.25 = -9.620940702 Reorder the terms: -0.25 + x = -9.620940702 Solving -0.25 + x = -9.620940702 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 = -9.620940702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -9.620940702 + 0.25 x = -9.620940702 + 0.25 Combine like terms: -9.620940702 + 0.25 = -9.370940702 x = -9.370940702 Simplifying x = -9.370940702

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.870940702, -9.370940702}

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