2x^2-71x+108=0

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Solution for 2x^2-71x+108=0 equation: 


Simplifying
2x2 + -71x + 108 = 0

Reorder the terms:
108 + -71x + 2x2 = 0

Solving
108 + -71x + 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'.
54 + -35.5x + x2 = 0

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + -35.5x + -54 + x2 = 0 + -54

Reorder the terms:
54 + -54 + -35.5x + x2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -35.5x + x2 = 0 + -54
-35.5x + x2 = 0 + -54

Combine like terms: 0 + -54 = -54
-35.5x + x2 = -54

The x term is -35.5x.  Take half its coefficient (-17.75).
Square it (315.0625) and add it to both sides.

Add '315.0625' to each side of the equation.
-35.5x + 315.0625 + x2 = -54 + 315.0625

Reorder the terms:
315.0625 + -35.5x + x2 = -54 + 315.0625

Combine like terms: -54 + 315.0625 = 261.0625
315.0625 + -35.5x + x2 = 261.0625

Factor a perfect square on the left side:
(x + -17.75)(x + -17.75) = 261.0625

Calculate the square root of the right side: 16.157428632

Break this problem into two subproblems by setting 
(x + -17.75) equal to 16.157428632 and -16.157428632.


Subproblem 1
x + -17.75 = 16.157428632

Simplifying
x + -17.75 = 16.157428632

Reorder the terms:
-17.75 + x = 16.157428632

Solving
-17.75 + x = 16.157428632

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '17.75' to each side of the equation.
-17.75 + 17.75 + x = 16.157428632 + 17.75

Combine like terms: -17.75 + 17.75 = 0.00
0.00 + x = 16.157428632 + 17.75
x = 16.157428632 + 17.75

Combine like terms: 16.157428632 + 17.75 = 33.907428632
x = 33.907428632

Simplifying
x = 33.907428632


Subproblem 2
x + -17.75 = -16.157428632

Simplifying
x + -17.75 = -16.157428632

Reorder the terms:
-17.75 + x = -16.157428632

Solving
-17.75 + x = -16.157428632

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '17.75' to each side of the equation.
-17.75 + 17.75 + x = -16.157428632 + 17.75

Combine like terms: -17.75 + 17.75 = 0.00
0.00 + x = -16.157428632 + 17.75
x = -16.157428632 + 17.75

Combine like terms: -16.157428632 + 17.75 = 1.592571368
x = 1.592571368

Simplifying
x = 1.592571368


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {33.907428632, 1.592571368}

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