1=2x^2-22x+61

Solution for 1=2x^2-22x+61 equation:

Simplifying
1 = 2x2 + -22x + 61

Reorder the terms:
1 = 61 + -22x + 2x2

Solving
1 = 61 + -22x + 2x2

Solving for variable 'x'.

Combine like terms: 1 + -61 = -60
-60 + 22x + -2x2 = 61 + -22x + 2x2 + -61 + 22x + -2x2

Reorder the terms:
-60 + 22x + -2x2 = 61 + -61 + -22x + 22x + 2x2 + -2x2

Combine like terms: 61 + -61 = 0
-60 + 22x + -2x2 = 0 + -22x + 22x + 2x2 + -2x2
-60 + 22x + -2x2 = -22x + 22x + 2x2 + -2x2

Combine like terms: -22x + 22x = 0
-60 + 22x + -2x2 = 0 + 2x2 + -2x2
-60 + 22x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-60 + 22x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 11x + -1x2) = 0

Factor a trinomial.
2((-6 + x)(5 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {6, 5}