3+x(33-x)=150

Solution for 3+x(33-x)=150 equation:

Simplifying
3 + x(33 + -1x) = 150
3 + (33 * x + -1x * x) = 150
3 + (33x + -1x2) = 150

Solving
3 + 33x + -1x2 = 150

Solving for variable 'x'.

Reorder the terms:
3 + -150 + 33x + -1x2 = 150 + -150

Combine like terms: 3 + -150 = -147
-147 + 33x + -1x2 = 150 + -150

Combine like terms: 150 + -150 = 0
-147 + 33x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
147 + -33x + x2 = 0

Move the constant term to the right:

Add '-147' to each side of the equation.
147 + -33x + -147 + x2 = 0 + -147

Reorder the terms:
147 + -147 + -33x + x2 = 0 + -147

Combine like terms: 147 + -147 = 0
0 + -33x + x2 = 0 + -147
-33x + x2 = 0 + -147

Combine like terms: 0 + -147 = -147
-33x + x2 = -147

The x term is -33x.  Take half its coefficient (-16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
-33x + 272.25 + x2 = -147 + 272.25

Reorder the terms:
272.25 + -33x + x2 = -147 + 272.25

Combine like terms: -147 + 272.25 = 125.25
272.25 + -33x + x2 = 125.25

Factor a perfect square on the left side:
(x + -16.5)(x + -16.5) = 125.25

Calculate the square root of the right side: 11.191514643

Break this problem into two subproblems by setting 
(x + -16.5) equal to 11.191514643 and -11.191514643.

Subproblem 1
x + -16.5 = 11.191514643

Simplifying
x + -16.5 = 11.191514643

Reorder the terms:
-16.5 + x = 11.191514643

Solving
-16.5 + x = 11.191514643

Solving for variable 'x'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + x = 11.191514643 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + x = 11.191514643 + 16.5
x = 11.191514643 + 16.5

Combine like terms: 11.191514643 + 16.5 = 27.691514643
x = 27.691514643

Simplifying
x = 27.691514643

Subproblem 2
x + -16.5 = -11.191514643

Simplifying
x + -16.5 = -11.191514643

Reorder the terms:
-16.5 + x = -11.191514643

Solving
-16.5 + x = -11.191514643

Solving for variable 'x'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + x = -11.191514643 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + x = -11.191514643 + 16.5
x = -11.191514643 + 16.5

Combine like terms: -11.191514643 + 16.5 = 5.308485357
x = 5.308485357

Simplifying
x = 5.308485357

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.691514643, 5.308485357}