3x^2-33x-5.3=0

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Solution for 3x^2-33x-5.3=0 equation:


Simplifying
3x2 + -33x + -5.3 = 0

Reorder the terms:
-5.3 + -33x + 3x2 = 0

Solving
-5.3 + -33x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-1.766666667 + -11x + x2 = 0

Move the constant term to the right:

Add '1.766666667' to each side of the equation.
-1.766666667 + -11x + 1.766666667 + x2 = 0 + 1.766666667

Reorder the terms:
-1.766666667 + 1.766666667 + -11x + x2 = 0 + 1.766666667

Combine like terms: -1.766666667 + 1.766666667 = 0.000000000
0.000000000 + -11x + x2 = 0 + 1.766666667
-11x + x2 = 0 + 1.766666667

Combine like terms: 0 + 1.766666667 = 1.766666667
-11x + x2 = 1.766666667

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 1.766666667 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 1.766666667 + 30.25

Combine like terms: 1.766666667 + 30.25 = 32.016666667
30.25 + -11x + x2 = 32.016666667

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 32.016666667

Calculate the square root of the right side: 5.658327197

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5.658327197 and -5.658327197.

Subproblem 1

x + -5.5 = 5.658327197 Simplifying x + -5.5 = 5.658327197 Reorder the terms: -5.5 + x = 5.658327197 Solving -5.5 + x = 5.658327197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.658327197 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.658327197 + 5.5 x = 5.658327197 + 5.5 Combine like terms: 5.658327197 + 5.5 = 11.158327197 x = 11.158327197 Simplifying x = 11.158327197

Subproblem 2

x + -5.5 = -5.658327197 Simplifying x + -5.5 = -5.658327197 Reorder the terms: -5.5 + x = -5.658327197 Solving -5.5 + x = -5.658327197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.658327197 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.658327197 + 5.5 x = -5.658327197 + 5.5 Combine like terms: -5.658327197 + 5.5 = -0.158327197 x = -0.158327197 Simplifying x = -0.158327197

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.158327197, -0.158327197}

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