x^2-33-15x=0

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Solution for x^2-33-15x=0 equation: 


Simplifying
x2 + -33 + -15x = 0

Reorder the terms:
-33 + -15x + x2 = 0

Solving
-33 + -15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -15x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + -15x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -15x + x2 = 0 + 33
-15x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
-15x + x2 = 33

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 33 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 33 + 56.25

Combine like terms: 33 + 56.25 = 89.25
56.25 + -15x + x2 = 89.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 89.25

Calculate the square root of the right side: 9.447221814

Break this problem into two subproblems by setting 
(x + -7.5) equal to 9.447221814 and -9.447221814.


Subproblem 1
x + -7.5 = 9.447221814

Simplifying
x + -7.5 = 9.447221814

Reorder the terms:
-7.5 + x = 9.447221814

Solving
-7.5 + x = 9.447221814

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 9.447221814 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 9.447221814 + 7.5
x = 9.447221814 + 7.5

Combine like terms: 9.447221814 + 7.5 = 16.947221814
x = 16.947221814

Simplifying
x = 16.947221814


Subproblem 2
x + -7.5 = -9.447221814

Simplifying
x + -7.5 = -9.447221814

Reorder the terms:
-7.5 + x = -9.447221814

Solving
-7.5 + x = -9.447221814

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -9.447221814 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -9.447221814 + 7.5
x = -9.447221814 + 7.5

Combine like terms: -9.447221814 + 7.5 = -1.947221814
x = -1.947221814

Simplifying
x = -1.947221814


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.947221814, -1.947221814}

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