2x^2-51x+6=0

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Solution for 2x^2-51x+6=0 equation:


Simplifying
2x2 + -51x + 6 = 0

Reorder the terms:
6 + -51x + 2x2 = 0

Solving
6 + -51x + 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'.
3 + -25.5x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -25.5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -25.5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -25.5x + x2 = 0 + -3
-25.5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-25.5x + x2 = -3

The x term is -25.5x.  Take half its coefficient (-12.75).
Square it (162.5625) and add it to both sides.

Add '162.5625' to each side of the equation.
-25.5x + 162.5625 + x2 = -3 + 162.5625

Reorder the terms:
162.5625 + -25.5x + x2 = -3 + 162.5625

Combine like terms: -3 + 162.5625 = 159.5625
162.5625 + -25.5x + x2 = 159.5625

Factor a perfect square on the left side:
(x + -12.75)(x + -12.75) = 159.5625

Calculate the square root of the right side: 12.631805097

Break this problem into two subproblems by setting 
(x + -12.75) equal to 12.631805097 and -12.631805097.

Subproblem 1

x + -12.75 = 12.631805097 Simplifying x + -12.75 = 12.631805097 Reorder the terms: -12.75 + x = 12.631805097 Solving -12.75 + x = 12.631805097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.75' to each side of the equation. -12.75 + 12.75 + x = 12.631805097 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + x = 12.631805097 + 12.75 x = 12.631805097 + 12.75 Combine like terms: 12.631805097 + 12.75 = 25.381805097 x = 25.381805097 Simplifying x = 25.381805097

Subproblem 2

x + -12.75 = -12.631805097 Simplifying x + -12.75 = -12.631805097 Reorder the terms: -12.75 + x = -12.631805097 Solving -12.75 + x = -12.631805097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.75' to each side of the equation. -12.75 + 12.75 + x = -12.631805097 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + x = -12.631805097 + 12.75 x = -12.631805097 + 12.75 Combine like terms: -12.631805097 + 12.75 = 0.118194903 x = 0.118194903 Simplifying x = 0.118194903

Solution

The solution to the problem is based on the solutions from the subproblems. x = {25.381805097, 0.118194903}

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