3x^2+18x+11=0

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Solution for 3x^2+18x+11=0 equation:


Simplifying
3x2 + 18x + 11 = 0

Reorder the terms:
11 + 18x + 3x2 = 0

Solving
11 + 18x + 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'.
3.666666667 + 6x + x2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + 6x + -3.666666667 + x2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + 6x + x2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + 6x + x2 = 0 + -3.666666667
6x + x2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
6x + x2 = -3.666666667

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 = -3.666666667 + 9

Reorder the terms:
9 + 6x + x2 = -3.666666667 + 9

Combine like terms: -3.666666667 + 9 = 5.333333333
9 + 6x + x2 = 5.333333333

Factor a perfect square on the left side:
(x + 3)(x + 3) = 5.333333333

Calculate the square root of the right side: 2.309401077

Break this problem into two subproblems by setting 
(x + 3) equal to 2.309401077 and -2.309401077.

Subproblem 1

x + 3 = 2.309401077 Simplifying x + 3 = 2.309401077 Reorder the terms: 3 + x = 2.309401077 Solving 3 + x = 2.309401077 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 = 2.309401077 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.309401077 + -3 x = 2.309401077 + -3 Combine like terms: 2.309401077 + -3 = -0.690598923 x = -0.690598923 Simplifying x = -0.690598923

Subproblem 2

x + 3 = -2.309401077 Simplifying x + 3 = -2.309401077 Reorder the terms: 3 + x = -2.309401077 Solving 3 + x = -2.309401077 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 = -2.309401077 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.309401077 + -3 x = -2.309401077 + -3 Combine like terms: -2.309401077 + -3 = -5.309401077 x = -5.309401077 Simplifying x = -5.309401077

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.690598923, -5.309401077}

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