2x^2+200x-150=0

Solution for 2x^2+200x-150=0 equation:

Simplifying
2x2 + 200x + -150 = 0

Reorder the terms:
-150 + 200x + 2x2 = 0

Solving
-150 + 200x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-75 + 100x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-75 + 100x + x2)' equal to zero and attempt to solve:

Simplifying
-75 + 100x + x2 = 0

Solving
-75 + 100x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 100x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 100x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 100x + x2 = 0 + 75
100x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
100x + x2 = 75

The x term is 100x.  Take half its coefficient (50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
100x + 2500 + x2 = 75 + 2500

Reorder the terms:
2500 + 100x + x2 = 75 + 2500

Combine like terms: 75 + 2500 = 2575
2500 + 100x + x2 = 2575

Factor a perfect square on the left side:
(x + 50)(x + 50) = 2575

Calculate the square root of the right side: 50.744457825

Break this problem into two subproblems by setting 
(x + 50) equal to 50.744457825 and -50.744457825.

Subproblem 1
x + 50 = 50.744457825

Simplifying
x + 50 = 50.744457825

Reorder the terms:
50 + x = 50.744457825

Solving
50 + x = 50.744457825

Solving for variable 'x'.

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

Add '-50' to each side of the equation.
50 + -50 + x = 50.744457825 + -50

Combine like terms: 50 + -50 = 0
0 + x = 50.744457825 + -50
x = 50.744457825 + -50

Combine like terms: 50.744457825 + -50 = 0.744457825
x = 0.744457825

Simplifying
x = 0.744457825

Subproblem 2
x + 50 = -50.744457825

Simplifying
x + 50 = -50.744457825

Reorder the terms:
50 + x = -50.744457825

Solving
50 + x = -50.744457825

Solving for variable 'x'.

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

Add '-50' to each side of the equation.
50 + -50 + x = -50.744457825 + -50

Combine like terms: 50 + -50 = 0
0 + x = -50.744457825 + -50
x = -50.744457825 + -50

Combine like terms: -50.744457825 + -50 = -100.744457825
x = -100.744457825

Simplifying
x = -100.744457825

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.744457825, -100.744457825}
Solution
x = {0.744457825, -100.744457825}