x^2+33x-450=0

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Solution for x^2+33x-450=0 equation: 


Simplifying
x2 + 33x + -450 = 0

Reorder the terms:
-450 + 33x + x2 = 0

Solving
-450 + 33x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '450' to each side of the equation.
-450 + 33x + 450 + x2 = 0 + 450

Reorder the terms:
-450 + 450 + 33x + x2 = 0 + 450

Combine like terms: -450 + 450 = 0
0 + 33x + x2 = 0 + 450
33x + x2 = 0 + 450

Combine like terms: 0 + 450 = 450
33x + x2 = 450

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 = 450 + 272.25

Reorder the terms:
272.25 + 33x + x2 = 450 + 272.25

Combine like terms: 450 + 272.25 = 722.25
272.25 + 33x + x2 = 722.25

Factor a perfect square on the left side:
(x + 16.5)(x + 16.5) = 722.25

Calculate the square root of the right side: 26.874709301

Break this problem into two subproblems by setting 
(x + 16.5) equal to 26.874709301 and -26.874709301.


Subproblem 1
x + 16.5 = 26.874709301

Simplifying
x + 16.5 = 26.874709301

Reorder the terms:
16.5 + x = 26.874709301

Solving
16.5 + x = 26.874709301

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 = 26.874709301 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + x = 26.874709301 + -16.5
x = 26.874709301 + -16.5

Combine like terms: 26.874709301 + -16.5 = 10.374709301
x = 10.374709301

Simplifying
x = 10.374709301


Subproblem 2
x + 16.5 = -26.874709301

Simplifying
x + 16.5 = -26.874709301

Reorder the terms:
16.5 + x = -26.874709301

Solving
16.5 + x = -26.874709301

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 = -26.874709301 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + x = -26.874709301 + -16.5
x = -26.874709301 + -16.5

Combine like terms: -26.874709301 + -16.5 = -43.374709301
x = -43.374709301

Simplifying
x = -43.374709301


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.374709301, -43.374709301}

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