2x^2-31x+16=0

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Solution for 2x^2-31x+16=0 equation: 


Simplifying
2x2 + -31x + 16 = 0

Reorder the terms:
16 + -31x + 2x2 = 0

Solving
16 + -31x + 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 + -15.5x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -15.5x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -15.5x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -15.5x + x2 = 0 + -8
-15.5x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-15.5x + x2 = -8

The x term is -15.5x.  Take half its coefficient (-7.75).
Square it (60.0625) and add it to both sides.

Add '60.0625' to each side of the equation.
-15.5x + 60.0625 + x2 = -8 + 60.0625

Reorder the terms:
60.0625 + -15.5x + x2 = -8 + 60.0625

Combine like terms: -8 + 60.0625 = 52.0625
60.0625 + -15.5x + x2 = 52.0625

Factor a perfect square on the left side:
(x + -7.75)(x + -7.75) = 52.0625

Calculate the square root of the right side: 7.215434845

Break this problem into two subproblems by setting 
(x + -7.75) equal to 7.215434845 and -7.215434845.


Subproblem 1
x + -7.75 = 7.215434845

Simplifying
x + -7.75 = 7.215434845

Reorder the terms:
-7.75 + x = 7.215434845

Solving
-7.75 + x = 7.215434845

Solving for variable 'x'.

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

Add '7.75' to each side of the equation.
-7.75 + 7.75 + x = 7.215434845 + 7.75

Combine like terms: -7.75 + 7.75 = 0.00
0.00 + x = 7.215434845 + 7.75
x = 7.215434845 + 7.75

Combine like terms: 7.215434845 + 7.75 = 14.965434845
x = 14.965434845

Simplifying
x = 14.965434845


Subproblem 2
x + -7.75 = -7.215434845

Simplifying
x + -7.75 = -7.215434845

Reorder the terms:
-7.75 + x = -7.215434845

Solving
-7.75 + x = -7.215434845

Solving for variable 'x'.

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

Add '7.75' to each side of the equation.
-7.75 + 7.75 + x = -7.215434845 + 7.75

Combine like terms: -7.75 + 7.75 = 0.00
0.00 + x = -7.215434845 + 7.75
x = -7.215434845 + 7.75

Combine like terms: -7.215434845 + 7.75 = 0.534565155
x = 0.534565155

Simplifying
x = 0.534565155


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.965434845, 0.534565155}

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