x^2-10x-33=0

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Solution for x^2-10x-33=0 equation: 


Simplifying
x2 + -10x + -33 = 0

Reorder the terms:
-33 + -10x + x2 = 0

Solving
-33 + -10x + 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 + -10x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + -10x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -10x + x2 = 0 + 33
-10x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
-10x + x2 = 33

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 33 + 25

Reorder the terms:
25 + -10x + x2 = 33 + 25

Combine like terms: 33 + 25 = 58
25 + -10x + x2 = 58

Factor a perfect square on the left side:
(x + -5)(x + -5) = 58

Calculate the square root of the right side: 7.615773106

Break this problem into two subproblems by setting 
(x + -5) equal to 7.615773106 and -7.615773106.


Subproblem 1
x + -5 = 7.615773106

Simplifying
x + -5 = 7.615773106

Reorder the terms:
-5 + x = 7.615773106

Solving
-5 + x = 7.615773106

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 7.615773106 + 5

Combine like terms: -5 + 5 = 0
0 + x = 7.615773106 + 5
x = 7.615773106 + 5

Combine like terms: 7.615773106 + 5 = 12.615773106
x = 12.615773106

Simplifying
x = 12.615773106


Subproblem 2
x + -5 = -7.615773106

Simplifying
x + -5 = -7.615773106

Reorder the terms:
-5 + x = -7.615773106

Solving
-5 + x = -7.615773106

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -7.615773106 + 5

Combine like terms: -5 + 5 = 0
0 + x = -7.615773106 + 5
x = -7.615773106 + 5

Combine like terms: -7.615773106 + 5 = -2.615773106
x = -2.615773106

Simplifying
x = -2.615773106


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.615773106, -2.615773106}

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