2x^2-41x-14=0

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Solution for 2x^2-41x-14=0 equation:


Simplifying
2x2 + -41x + -14 = 0

Reorder the terms:
-14 + -41x + 2x2 = 0

Solving
-14 + -41x + 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'.
-7 + -20.5x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -20.5x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -20.5x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -20.5x + x2 = 0 + 7
-20.5x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-20.5x + x2 = 7

The x term is -20.5x.  Take half its coefficient (-10.25).
Square it (105.0625) and add it to both sides.

Add '105.0625' to each side of the equation.
-20.5x + 105.0625 + x2 = 7 + 105.0625

Reorder the terms:
105.0625 + -20.5x + x2 = 7 + 105.0625

Combine like terms: 7 + 105.0625 = 112.0625
105.0625 + -20.5x + x2 = 112.0625

Factor a perfect square on the left side:
(x + -10.25)(x + -10.25) = 112.0625

Calculate the square root of the right side: 10.58595768

Break this problem into two subproblems by setting 
(x + -10.25) equal to 10.58595768 and -10.58595768.

Subproblem 1

x + -10.25 = 10.58595768 Simplifying x + -10.25 = 10.58595768 Reorder the terms: -10.25 + x = 10.58595768 Solving -10.25 + x = 10.58595768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.25' to each side of the equation. -10.25 + 10.25 + x = 10.58595768 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + x = 10.58595768 + 10.25 x = 10.58595768 + 10.25 Combine like terms: 10.58595768 + 10.25 = 20.83595768 x = 20.83595768 Simplifying x = 20.83595768

Subproblem 2

x + -10.25 = -10.58595768 Simplifying x + -10.25 = -10.58595768 Reorder the terms: -10.25 + x = -10.58595768 Solving -10.25 + x = -10.58595768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.25' to each side of the equation. -10.25 + 10.25 + x = -10.58595768 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + x = -10.58595768 + 10.25 x = -10.58595768 + 10.25 Combine like terms: -10.58595768 + 10.25 = -0.33595768 x = -0.33595768 Simplifying x = -0.33595768

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.83595768, -0.33595768}

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