2x^2-59x+17=0

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Solution for 2x^2-59x+17=0 equation:


Simplifying
2x2 + -59x + 17 = 0

Reorder the terms:
17 + -59x + 2x2 = 0

Solving
17 + -59x + 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'.
8.5 + -29.5x + x2 = 0

Move the constant term to the right:

Add '-8.5' to each side of the equation.
8.5 + -29.5x + -8.5 + x2 = 0 + -8.5

Reorder the terms:
8.5 + -8.5 + -29.5x + x2 = 0 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + -29.5x + x2 = 0 + -8.5
-29.5x + x2 = 0 + -8.5

Combine like terms: 0 + -8.5 = -8.5
-29.5x + x2 = -8.5

The x term is -29.5x.  Take half its coefficient (-14.75).
Square it (217.5625) and add it to both sides.

Add '217.5625' to each side of the equation.
-29.5x + 217.5625 + x2 = -8.5 + 217.5625

Reorder the terms:
217.5625 + -29.5x + x2 = -8.5 + 217.5625

Combine like terms: -8.5 + 217.5625 = 209.0625
217.5625 + -29.5x + x2 = 209.0625

Factor a perfect square on the left side:
(x + -14.75)(x + -14.75) = 209.0625

Calculate the square root of the right side: 14.458993741

Break this problem into two subproblems by setting 
(x + -14.75) equal to 14.458993741 and -14.458993741.

Subproblem 1

x + -14.75 = 14.458993741 Simplifying x + -14.75 = 14.458993741 Reorder the terms: -14.75 + x = 14.458993741 Solving -14.75 + x = 14.458993741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + x = 14.458993741 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + x = 14.458993741 + 14.75 x = 14.458993741 + 14.75 Combine like terms: 14.458993741 + 14.75 = 29.208993741 x = 29.208993741 Simplifying x = 29.208993741

Subproblem 2

x + -14.75 = -14.458993741 Simplifying x + -14.75 = -14.458993741 Reorder the terms: -14.75 + x = -14.458993741 Solving -14.75 + x = -14.458993741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + x = -14.458993741 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + x = -14.458993741 + 14.75 x = -14.458993741 + 14.75 Combine like terms: -14.458993741 + 14.75 = 0.291006259 x = 0.291006259 Simplifying x = 0.291006259

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.208993741, 0.291006259}

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