2x^2-33x+31=0

Solution for 2x^2-33x+31=0 equation:

Simplifying
2x2 + -33x + 31 = 0

Reorder the terms:
31 + -33x + 2x2 = 0

Solving
31 + -33x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(31 + -2x) = 0

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(31 + -2x)' equal to zero and attempt to solve:

Simplifying
31 + -2x = 0

Solving
31 + -2x = 0

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

Add '-31' to each side of the equation.
31 + -31 + -2x = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -2x = 0 + -31
-2x = 0 + -31

Combine like terms: 0 + -31 = -31
-2x = -31

Divide each side by '-2'.
x = 15.5

Simplifying
x = 15.5
Solution
x = {1, 15.5}