2x^2+250x-4=0

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Solution for 2x^2+250x-4=0 equation: 


Simplifying
2x2 + 250x + -4 = 0

Reorder the terms:
-4 + 250x + 2x2 = 0

Solving
-4 + 250x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 125x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 125x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + 125x + x2 = 0

Solving
-2 + 125x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 125x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 125x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 125x + x2 = 0 + 2
125x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
125x + x2 = 2

The x term is 125x.  Take half its coefficient (62.5).
Square it (3906.25) and add it to both sides.

Add '3906.25' to each side of the equation.
125x + 3906.25 + x2 = 2 + 3906.25

Reorder the terms:
3906.25 + 125x + x2 = 2 + 3906.25

Combine like terms: 2 + 3906.25 = 3908.25
3906.25 + 125x + x2 = 3908.25

Factor a perfect square on the left side:
(x + 62.5)(x + 62.5) = 3908.25

Calculate the square root of the right side: 62.515997953

Break this problem into two subproblems by setting 
(x + 62.5) equal to 62.515997953 and -62.515997953.


Subproblem 1
x + 62.5 = 62.515997953

Simplifying
x + 62.5 = 62.515997953

Reorder the terms:
62.5 + x = 62.515997953

Solving
62.5 + x = 62.515997953

Solving for variable 'x'.

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

Add '-62.5' to each side of the equation.
62.5 + -62.5 + x = 62.515997953 + -62.5

Combine like terms: 62.5 + -62.5 = 0.0
0.0 + x = 62.515997953 + -62.5
x = 62.515997953 + -62.5

Combine like terms: 62.515997953 + -62.5 = 0.015997953
x = 0.015997953

Simplifying
x = 0.015997953


Subproblem 2
x + 62.5 = -62.515997953

Simplifying
x + 62.5 = -62.515997953

Reorder the terms:
62.5 + x = -62.515997953

Solving
62.5 + x = -62.515997953

Solving for variable 'x'.

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

Add '-62.5' to each side of the equation.
62.5 + -62.5 + x = -62.515997953 + -62.5

Combine like terms: 62.5 + -62.5 = 0.0
0.0 + x = -62.515997953 + -62.5
x = -62.515997953 + -62.5

Combine like terms: -62.515997953 + -62.5 = -125.015997953
x = -125.015997953

Simplifying
x = -125.015997953


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.015997953, -125.015997953}
Solution
x = {0.015997953, -125.015997953}

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