-2x^2+92x-290=0

Solution for -2x^2+92x-290=0 equation:

Simplifying
-2x2 + 92x + -290 = 0

Reorder the terms:
-290 + 92x + -2x2 = 0

Solving
-290 + 92x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-145 + 46x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-145 + 46x + -1x2)' equal to zero and attempt to solve:

Simplifying
-145 + 46x + -1x2 = 0

Solving
-145 + 46x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
145 + -46x + x2 = 0

Move the constant term to the right:

Add '-145' to each side of the equation.
145 + -46x + -145 + x2 = 0 + -145

Reorder the terms:
145 + -145 + -46x + x2 = 0 + -145

Combine like terms: 145 + -145 = 0
0 + -46x + x2 = 0 + -145
-46x + x2 = 0 + -145

Combine like terms: 0 + -145 = -145
-46x + x2 = -145

The x term is -46x.  Take half its coefficient (-23).
Square it (529) and add it to both sides.

Add '529' to each side of the equation.
-46x + 529 + x2 = -145 + 529

Reorder the terms:
529 + -46x + x2 = -145 + 529

Combine like terms: -145 + 529 = 384
529 + -46x + x2 = 384

Factor a perfect square on the left side:
(x + -23)(x + -23) = 384

Calculate the square root of the right side: 19.595917942

Break this problem into two subproblems by setting 
(x + -23) equal to 19.595917942 and -19.595917942.

Subproblem 1
x + -23 = 19.595917942

Simplifying
x + -23 = 19.595917942

Reorder the terms:
-23 + x = 19.595917942

Solving
-23 + x = 19.595917942

Solving for variable 'x'.

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

Add '23' to each side of the equation.
-23 + 23 + x = 19.595917942 + 23

Combine like terms: -23 + 23 = 0
0 + x = 19.595917942 + 23
x = 19.595917942 + 23

Combine like terms: 19.595917942 + 23 = 42.595917942
x = 42.595917942

Simplifying
x = 42.595917942

Subproblem 2
x + -23 = -19.595917942

Simplifying
x + -23 = -19.595917942

Reorder the terms:
-23 + x = -19.595917942

Solving
-23 + x = -19.595917942

Solving for variable 'x'.

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

Add '23' to each side of the equation.
-23 + 23 + x = -19.595917942 + 23

Combine like terms: -23 + 23 = 0
0 + x = -19.595917942 + 23
x = -19.595917942 + 23

Combine like terms: -19.595917942 + 23 = 3.404082058
x = 3.404082058

Simplifying
x = 3.404082058

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.595917942, 3.404082058}
Solution
x = {42.595917942, 3.404082058}