150=-2x^2+60x-200

Solution for 150=-2x^2+60x-200 equation:

Simplifying
150 = -2x2 + 60x + -200

Reorder the terms:
150 = -200 + 60x + -2x2

Solving
150 = -200 + 60x + -2x2

Solving for variable 'x'.

Combine like terms: 150 + 200 = 350
350 + -60x + 2x2 = -200 + 60x + -2x2 + 200 + -60x + 2x2

Reorder the terms:
350 + -60x + 2x2 = -200 + 200 + 60x + -60x + -2x2 + 2x2

Combine like terms: -200 + 200 = 0
350 + -60x + 2x2 = 0 + 60x + -60x + -2x2 + 2x2
350 + -60x + 2x2 = 60x + -60x + -2x2 + 2x2

Combine like terms: 60x + -60x = 0
350 + -60x + 2x2 = 0 + -2x2 + 2x2
350 + -60x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
350 + -60x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(175 + -30x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(175 + -30x + x2)' equal to zero and attempt to solve:

Simplifying
175 + -30x + x2 = 0

Solving
175 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-175' to each side of the equation.
175 + -30x + -175 + x2 = 0 + -175

Reorder the terms:
175 + -175 + -30x + x2 = 0 + -175

Combine like terms: 175 + -175 = 0
0 + -30x + x2 = 0 + -175
-30x + x2 = 0 + -175

Combine like terms: 0 + -175 = -175
-30x + x2 = -175

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -175 + 225

Reorder the terms:
225 + -30x + x2 = -175 + 225

Combine like terms: -175 + 225 = 50
225 + -30x + x2 = 50

Factor a perfect square on the left side:
(x + -15)(x + -15) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(x + -15) equal to 7.071067812 and -7.071067812.

Subproblem 1
x + -15 = 7.071067812

Simplifying
x + -15 = 7.071067812

Reorder the terms:
-15 + x = 7.071067812

Solving
-15 + x = 7.071067812

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 7.071067812 + 15

Combine like terms: -15 + 15 = 0
0 + x = 7.071067812 + 15
x = 7.071067812 + 15

Combine like terms: 7.071067812 + 15 = 22.071067812
x = 22.071067812

Simplifying
x = 22.071067812

Subproblem 2
x + -15 = -7.071067812

Simplifying
x + -15 = -7.071067812

Reorder the terms:
-15 + x = -7.071067812

Solving
-15 + x = -7.071067812

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -7.071067812 + 15

Combine like terms: -15 + 15 = 0
0 + x = -7.071067812 + 15
x = -7.071067812 + 15

Combine like terms: -7.071067812 + 15 = 7.928932188
x = 7.928932188

Simplifying
x = 7.928932188

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.071067812, 7.928932188}
Solution
x = {22.071067812, 7.928932188}