-2x^2+80x+350=0

Solution for -2x^2+80x+350=0 equation:

Simplifying
-2x2 + 80x + 350 = 0

Reorder the terms:
350 + 80x + -2x2 = 0

Solving
350 + 80x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(175 + 40x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(175 + 40x + -1x2)' equal to zero and attempt to solve:

Simplifying
175 + 40x + -1x2 = 0

Solving
175 + 40x + -1x2 = 0

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

Divide each side by '-1'.
-175 + -40x + x2 = 0

Move the constant term to the right:

Add '175' to each side of the equation.
-175 + -40x + 175 + x2 = 0 + 175

Reorder the terms:
-175 + 175 + -40x + x2 = 0 + 175

Combine like terms: -175 + 175 = 0
0 + -40x + x2 = 0 + 175
-40x + x2 = 0 + 175

Combine like terms: 0 + 175 = 175
-40x + x2 = 175

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = 175 + 400

Reorder the terms:
400 + -40x + x2 = 175 + 400

Combine like terms: 175 + 400 = 575
400 + -40x + x2 = 575

Factor a perfect square on the left side:
(x + -20)(x + -20) = 575

Calculate the square root of the right side: 23.979157617

Break this problem into two subproblems by setting 
(x + -20) equal to 23.979157617 and -23.979157617.

Subproblem 1
x + -20 = 23.979157617

Simplifying
x + -20 = 23.979157617

Reorder the terms:
-20 + x = 23.979157617

Solving
-20 + x = 23.979157617

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = 23.979157617 + 20

Combine like terms: -20 + 20 = 0
0 + x = 23.979157617 + 20
x = 23.979157617 + 20

Combine like terms: 23.979157617 + 20 = 43.979157617
x = 43.979157617

Simplifying
x = 43.979157617

Subproblem 2
x + -20 = -23.979157617

Simplifying
x + -20 = -23.979157617

Reorder the terms:
-20 + x = -23.979157617

Solving
-20 + x = -23.979157617

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = -23.979157617 + 20

Combine like terms: -20 + 20 = 0
0 + x = -23.979157617 + 20
x = -23.979157617 + 20

Combine like terms: -23.979157617 + 20 = -3.979157617
x = -3.979157617

Simplifying
x = -3.979157617

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {43.979157617, -3.979157617}
Solution
x = {43.979157617, -3.979157617}