11x^2+66x-309=0

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Solution for 11x^2+66x-309=0 equation:


Simplifying
11x2 + 66x + -309 = 0

Reorder the terms:
-309 + 66x + 11x2 = 0

Solving
-309 + 66x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
-28.09090909 + 6x + x2 = 0

Move the constant term to the right:

Add '28.09090909' to each side of the equation.
-28.09090909 + 6x + 28.09090909 + x2 = 0 + 28.09090909

Reorder the terms:
-28.09090909 + 28.09090909 + 6x + x2 = 0 + 28.09090909

Combine like terms: -28.09090909 + 28.09090909 = 0.00000000
0.00000000 + 6x + x2 = 0 + 28.09090909
6x + x2 = 0 + 28.09090909

Combine like terms: 0 + 28.09090909 = 28.09090909
6x + x2 = 28.09090909

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 28.09090909 + 9

Reorder the terms:
9 + 6x + x2 = 28.09090909 + 9

Combine like terms: 28.09090909 + 9 = 37.09090909
9 + 6x + x2 = 37.09090909

Factor a perfect square on the left side:
(x + 3)(x + 3) = 37.09090909

Calculate the square root of the right side: 6.090230627

Break this problem into two subproblems by setting 
(x + 3) equal to 6.090230627 and -6.090230627.

Subproblem 1

x + 3 = 6.090230627 Simplifying x + 3 = 6.090230627 Reorder the terms: 3 + x = 6.090230627 Solving 3 + x = 6.090230627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.090230627 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.090230627 + -3 x = 6.090230627 + -3 Combine like terms: 6.090230627 + -3 = 3.090230627 x = 3.090230627 Simplifying x = 3.090230627

Subproblem 2

x + 3 = -6.090230627 Simplifying x + 3 = -6.090230627 Reorder the terms: 3 + x = -6.090230627 Solving 3 + x = -6.090230627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.090230627 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.090230627 + -3 x = -6.090230627 + -3 Combine like terms: -6.090230627 + -3 = -9.090230627 x = -9.090230627 Simplifying x = -9.090230627

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.090230627, -9.090230627}

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