9x^2-3x-11=0

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Solution for 9x^2-3x-11=0 equation:


Simplifying
9x2 + -3x + -11 = 0

Reorder the terms:
-11 + -3x + 9x2 = 0

Solving
-11 + -3x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-1.222222222 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '1.222222222' to each side of the equation.
-1.222222222 + -0.3333333333x + 1.222222222 + x2 = 0 + 1.222222222

Reorder the terms:
-1.222222222 + 1.222222222 + -0.3333333333x + x2 = 0 + 1.222222222

Combine like terms: -1.222222222 + 1.222222222 = 0.000000000
0.000000000 + -0.3333333333x + x2 = 0 + 1.222222222
-0.3333333333x + x2 = 0 + 1.222222222

Combine like terms: 0 + 1.222222222 = 1.222222222
-0.3333333333x + x2 = 1.222222222

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 1.222222222 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 1.222222222 + 0.02777777779

Combine like terms: 1.222222222 + 0.02777777779 = 1.24999999979
0.02777777779 + -0.3333333333x + x2 = 1.24999999979

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 1.24999999979

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + -0.1666666667 = 1.118033989 Simplifying x + -0.1666666667 = 1.118033989 Reorder the terms: -0.1666666667 + x = 1.118033989 Solving -0.1666666667 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 1.118033989 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 1.118033989 + 0.1666666667 x = 1.118033989 + 0.1666666667 Combine like terms: 1.118033989 + 0.1666666667 = 1.2847006557 x = 1.2847006557 Simplifying x = 1.2847006557

Subproblem 2

x + -0.1666666667 = -1.118033989 Simplifying x + -0.1666666667 = -1.118033989 Reorder the terms: -0.1666666667 + x = -1.118033989 Solving -0.1666666667 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -1.118033989 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -1.118033989 + 0.1666666667 x = -1.118033989 + 0.1666666667 Combine like terms: -1.118033989 + 0.1666666667 = -0.9513673223 x = -0.9513673223 Simplifying x = -0.9513673223

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2847006557, -0.9513673223}

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