2x^2+150x-7900=0

Solution for 2x^2+150x-7900=0 equation:

Simplifying
2x2 + 150x + -7900 = 0

Reorder the terms:
-7900 + 150x + 2x2 = 0

Solving
-7900 + 150x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3950 + 75x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3950 + 75x + x2)' equal to zero and attempt to solve:

Simplifying
-3950 + 75x + x2 = 0

Solving
-3950 + 75x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3950' to each side of the equation.
-3950 + 75x + 3950 + x2 = 0 + 3950

Reorder the terms:
-3950 + 3950 + 75x + x2 = 0 + 3950

Combine like terms: -3950 + 3950 = 0
0 + 75x + x2 = 0 + 3950
75x + x2 = 0 + 3950

Combine like terms: 0 + 3950 = 3950
75x + x2 = 3950

The x term is 75x.  Take half its coefficient (37.5).
Square it (1406.25) and add it to both sides.

Add '1406.25' to each side of the equation.
75x + 1406.25 + x2 = 3950 + 1406.25

Reorder the terms:
1406.25 + 75x + x2 = 3950 + 1406.25

Combine like terms: 3950 + 1406.25 = 5356.25
1406.25 + 75x + x2 = 5356.25

Factor a perfect square on the left side:
(x + 37.5)(x + 37.5) = 5356.25

Calculate the square root of the right side: 73.186405842

Break this problem into two subproblems by setting 
(x + 37.5) equal to 73.186405842 and -73.186405842.

Subproblem 1
x + 37.5 = 73.186405842

Simplifying
x + 37.5 = 73.186405842

Reorder the terms:
37.5 + x = 73.186405842

Solving
37.5 + x = 73.186405842

Solving for variable 'x'.

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

Add '-37.5' to each side of the equation.
37.5 + -37.5 + x = 73.186405842 + -37.5

Combine like terms: 37.5 + -37.5 = 0.0
0.0 + x = 73.186405842 + -37.5
x = 73.186405842 + -37.5

Combine like terms: 73.186405842 + -37.5 = 35.686405842
x = 35.686405842

Simplifying
x = 35.686405842

Subproblem 2
x + 37.5 = -73.186405842

Simplifying
x + 37.5 = -73.186405842

Reorder the terms:
37.5 + x = -73.186405842

Solving
37.5 + x = -73.186405842

Solving for variable 'x'.

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

Add '-37.5' to each side of the equation.
37.5 + -37.5 + x = -73.186405842 + -37.5

Combine like terms: 37.5 + -37.5 = 0.0
0.0 + x = -73.186405842 + -37.5
x = -73.186405842 + -37.5

Combine like terms: -73.186405842 + -37.5 = -110.686405842
x = -110.686405842

Simplifying
x = -110.686405842

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.686405842, -110.686405842}
Solution
x = {35.686405842, -110.686405842}