-2x^2+302x-1990=0

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Solution for -2x^2+302x-1990=0 equation: 


Simplifying
-2x2 + 302x + -1990 = 0

Reorder the terms:
-1990 + 302x + -2x2 = 0

Solving
-1990 + 302x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-995 + 151x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-995 + 151x + -1x2)' equal to zero and attempt to solve:

Simplifying
-995 + 151x + -1x2 = 0

Solving
-995 + 151x + -1x2 = 0

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

Divide each side by '-1'.
995 + -151x + x2 = 0

Move the constant term to the right:

Add '-995' to each side of the equation.
995 + -151x + -995 + x2 = 0 + -995

Reorder the terms:
995 + -995 + -151x + x2 = 0 + -995

Combine like terms: 995 + -995 = 0
0 + -151x + x2 = 0 + -995
-151x + x2 = 0 + -995

Combine like terms: 0 + -995 = -995
-151x + x2 = -995

The x term is -151x.  Take half its coefficient (-75.5).
Square it (5700.25) and add it to both sides.

Add '5700.25' to each side of the equation.
-151x + 5700.25 + x2 = -995 + 5700.25

Reorder the terms:
5700.25 + -151x + x2 = -995 + 5700.25

Combine like terms: -995 + 5700.25 = 4705.25
5700.25 + -151x + x2 = 4705.25

Factor a perfect square on the left side:
(x + -75.5)(x + -75.5) = 4705.25

Calculate the square root of the right side: 68.594824878

Break this problem into two subproblems by setting 
(x + -75.5) equal to 68.594824878 and -68.594824878.


Subproblem 1
x + -75.5 = 68.594824878

Simplifying
x + -75.5 = 68.594824878

Reorder the terms:
-75.5 + x = 68.594824878

Solving
-75.5 + x = 68.594824878

Solving for variable 'x'.

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

Add '75.5' to each side of the equation.
-75.5 + 75.5 + x = 68.594824878 + 75.5

Combine like terms: -75.5 + 75.5 = 0.0
0.0 + x = 68.594824878 + 75.5
x = 68.594824878 + 75.5

Combine like terms: 68.594824878 + 75.5 = 144.094824878
x = 144.094824878

Simplifying
x = 144.094824878


Subproblem 2
x + -75.5 = -68.594824878

Simplifying
x + -75.5 = -68.594824878

Reorder the terms:
-75.5 + x = -68.594824878

Solving
-75.5 + x = -68.594824878

Solving for variable 'x'.

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

Add '75.5' to each side of the equation.
-75.5 + 75.5 + x = -68.594824878 + 75.5

Combine like terms: -75.5 + 75.5 = 0.0
0.0 + x = -68.594824878 + 75.5
x = -68.594824878 + 75.5

Combine like terms: -68.594824878 + 75.5 = 6.905175122
x = 6.905175122

Simplifying
x = 6.905175122


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {144.094824878, 6.905175122}
Solution
x = {144.094824878, 6.905175122}

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