-2x^2+100x+40=0

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Solution for -2x^2+100x+40=0 equation: 


Simplifying
-2x2 + 100x + 40 = 0

Reorder the terms:
40 + 100x + -2x2 = 0

Solving
40 + 100x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + 50x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(20 + 50x + -1x2)' equal to zero and attempt to solve:

Simplifying
20 + 50x + -1x2 = 0

Solving
20 + 50x + -1x2 = 0

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

Divide each side by '-1'.
-20 + -50x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -50x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -50x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -50x + x2 = 0 + 20
-50x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-50x + x2 = 20

The x term is -50x.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50x + 625 + x2 = 20 + 625

Reorder the terms:
625 + -50x + x2 = 20 + 625

Combine like terms: 20 + 625 = 645
625 + -50x + x2 = 645

Factor a perfect square on the left side:
(x + -25)(x + -25) = 645

Calculate the square root of the right side: 25.396850198

Break this problem into two subproblems by setting 
(x + -25) equal to 25.396850198 and -25.396850198.


Subproblem 1
x + -25 = 25.396850198

Simplifying
x + -25 = 25.396850198

Reorder the terms:
-25 + x = 25.396850198

Solving
-25 + x = 25.396850198

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = 25.396850198 + 25

Combine like terms: -25 + 25 = 0
0 + x = 25.396850198 + 25
x = 25.396850198 + 25

Combine like terms: 25.396850198 + 25 = 50.396850198
x = 50.396850198

Simplifying
x = 50.396850198


Subproblem 2
x + -25 = -25.396850198

Simplifying
x + -25 = -25.396850198

Reorder the terms:
-25 + x = -25.396850198

Solving
-25 + x = -25.396850198

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + x = -25.396850198 + 25

Combine like terms: -25 + 25 = 0
0 + x = -25.396850198 + 25
x = -25.396850198 + 25

Combine like terms: -25.396850198 + 25 = -0.396850198
x = -0.396850198

Simplifying
x = -0.396850198


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.396850198, -0.396850198}
Solution
x = {50.396850198, -0.396850198}

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