2x^2+50x-20=0

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Solution for 2x^2+50x-20=0 equation: 


Simplifying
2x2 + 50x + -20 = 0

Reorder the terms:
-20 + 50x + 2x2 = 0

Solving
-20 + 50x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 25x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + 25x + x2)' equal to zero and attempt to solve:

Simplifying
-10 + 25x + x2 = 0

Solving
-10 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 25x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 25x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 25x + x2 = 0 + 10
25x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
25x + x2 = 10

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 10 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 10 + 156.25

Combine like terms: 10 + 156.25 = 166.25
156.25 + 25x + x2 = 166.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 166.25

Calculate the square root of the right side: 12.893796958

Break this problem into two subproblems by setting 
(x + 12.5) equal to 12.893796958 and -12.893796958.


Subproblem 1
x + 12.5 = 12.893796958

Simplifying
x + 12.5 = 12.893796958

Reorder the terms:
12.5 + x = 12.893796958

Solving
12.5 + x = 12.893796958

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 12.893796958 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 12.893796958 + -12.5
x = 12.893796958 + -12.5

Combine like terms: 12.893796958 + -12.5 = 0.393796958
x = 0.393796958

Simplifying
x = 0.393796958


Subproblem 2
x + 12.5 = -12.893796958

Simplifying
x + 12.5 = -12.893796958

Reorder the terms:
12.5 + x = -12.893796958

Solving
12.5 + x = -12.893796958

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -12.893796958 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -12.893796958 + -12.5
x = -12.893796958 + -12.5

Combine like terms: -12.893796958 + -12.5 = -25.393796958
x = -25.393796958

Simplifying
x = -25.393796958


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.393796958, -25.393796958}
Solution
x = {0.393796958, -25.393796958}

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