150x+x^2=10000

Solution for 150x+x^2=10000 equation:

Simplifying
150x + x2 = 10000

Solving
150x + x2 = 10000

Solving for variable 'x'.

Reorder the terms:
-10000 + 150x + x2 = 10000 + -10000

Combine like terms: 10000 + -10000 = 0
-10000 + 150x + x2 = 0

Factor a trinomial.
(-200 + -1x)(50 + -1x) = 0

Subproblem 1
Set the factor '(-200 + -1x)' equal to zero and attempt to solve:

Simplifying
-200 + -1x = 0

Solving
-200 + -1x = 0

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

Add '200' to each side of the equation.
-200 + 200 + -1x = 0 + 200

Combine like terms: -200 + 200 = 0
0 + -1x = 0 + 200
-1x = 0 + 200

Combine like terms: 0 + 200 = 200
-1x = 200

Divide each side by '-1'.
x = -200

Simplifying
x = -200
Subproblem 2
Set the factor '(50 + -1x)' equal to zero and attempt to solve:

Simplifying
50 + -1x = 0

Solving
50 + -1x = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1x = 0 + -50
-1x = 0 + -50

Combine like terms: 0 + -50 = -50
-1x = -50

Divide each side by '-1'.
x = 50

Simplifying
x = 50
Solution
x = {-200, 50}