2x^2+250x+5000=0

Solution for 2x^2+250x+5000=0 equation:

Simplifying
2x2 + 250x + 5000 = 0

Reorder the terms:
5000 + 250x + 2x2 = 0

Solving
5000 + 250x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2500 + 125x + x2) = 0

Factor a trinomial.
2((100 + x)(25 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(100 + x)' equal to zero and attempt to solve:

Simplifying
100 + x = 0

Solving
100 + x = 0

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

Add '-100' to each side of the equation.
100 + -100 + x = 0 + -100

Combine like terms: 100 + -100 = 0
0 + x = 0 + -100
x = 0 + -100

Combine like terms: 0 + -100 = -100
x = -100

Simplifying
x = -100
Subproblem 2
Set the factor '(25 + x)' equal to zero and attempt to solve:

Simplifying
25 + x = 0

Solving
25 + x = 0

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 = 0 + -25

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

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

Simplifying
x = -25
Solution
x = {-100, -25}