0=x^2+10x+33

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


Simplifying
0 = x2 + 10x + 33

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

Solving
0 = 33 + 10x + x2

Solving for variable 'x'.

Combine like terms: 0 + -33 = -33
-33 + -10x + -1x2 = 33 + 10x + x2 + -33 + -10x + -1x2

Reorder the terms:
-33 + -10x + -1x2 = 33 + -33 + 10x + -10x + x2 + -1x2

Combine like terms: 33 + -33 = 0
-33 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2
-33 + -10x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-33 + -10x + -1x2 = 0 + x2 + -1x2
-33 + -10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-33 + -10x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(33 + 10x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(33 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
33 + 10x + x2 = 0

Solving
33 + 10x + x2 = 0

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 = -8
25 + 10x + x2 = -8

Factor a perfect square on the left side:
(x + 5)(x + 5) = -8

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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