x^2+12x+33=0

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Solution for x^2+12x+33=0 equation:


Simplifying
x2 + 12x + 33 = 0

Reorder the terms:
33 + 12x + x2 = 0

Solving
33 + 12x + 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 + 12x + -33 + x2 = 0 + -33

Reorder the terms:
33 + -33 + 12x + x2 = 0 + -33

Combine like terms: 33 + -33 = 0
0 + 12x + x2 = 0 + -33
12x + x2 = 0 + -33

Combine like terms: 0 + -33 = -33
12x + x2 = -33

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -33 + 36

Reorder the terms:
36 + 12x + x2 = -33 + 36

Combine like terms: -33 + 36 = 3
36 + 12x + x2 = 3

Factor a perfect square on the left side:
(x + 6)(x + 6) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 6) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + 6 = 1.732050808 Simplifying x + 6 = 1.732050808 Reorder the terms: 6 + x = 1.732050808 Solving 6 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 1.732050808 + -6 Combine like terms: 6 + -6 = 0 0 + x = 1.732050808 + -6 x = 1.732050808 + -6 Combine like terms: 1.732050808 + -6 = -4.267949192 x = -4.267949192 Simplifying x = -4.267949192

Subproblem 2

x + 6 = -1.732050808 Simplifying x + 6 = -1.732050808 Reorder the terms: 6 + x = -1.732050808 Solving 6 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -1.732050808 + -6 Combine like terms: 6 + -6 = 0 0 + x = -1.732050808 + -6 x = -1.732050808 + -6 Combine like terms: -1.732050808 + -6 = -7.732050808 x = -7.732050808 Simplifying x = -7.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.267949192, -7.732050808}

 

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