9x^2-27x-26=0

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Solution for 9x^2-27x-26=0 equation:


Simplifying
9x2 + -27x + -26 = 0

Reorder the terms:
-26 + -27x + 9x2 = 0

Solving
-26 + -27x + 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'.
-2.888888889 + -3x + x2 = 0

Move the constant term to the right:

Add '2.888888889' to each side of the equation.
-2.888888889 + -3x + 2.888888889 + x2 = 0 + 2.888888889

Reorder the terms:
-2.888888889 + 2.888888889 + -3x + x2 = 0 + 2.888888889

Combine like terms: -2.888888889 + 2.888888889 = 0.000000000
0.000000000 + -3x + x2 = 0 + 2.888888889
-3x + x2 = 0 + 2.888888889

Combine like terms: 0 + 2.888888889 = 2.888888889
-3x + x2 = 2.888888889

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 2.888888889 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 2.888888889 + 2.25

Combine like terms: 2.888888889 + 2.25 = 5.138888889
2.25 + -3x + x2 = 5.138888889

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 5.138888889

Calculate the square root of the right side: 2.266911751

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.266911751 and -2.266911751.

Subproblem 1

x + -1.5 = 2.266911751 Simplifying x + -1.5 = 2.266911751 Reorder the terms: -1.5 + x = 2.266911751 Solving -1.5 + x = 2.266911751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.266911751 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.266911751 + 1.5 x = 2.266911751 + 1.5 Combine like terms: 2.266911751 + 1.5 = 3.766911751 x = 3.766911751 Simplifying x = 3.766911751

Subproblem 2

x + -1.5 = -2.266911751 Simplifying x + -1.5 = -2.266911751 Reorder the terms: -1.5 + x = -2.266911751 Solving -1.5 + x = -2.266911751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.266911751 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.266911751 + 1.5 x = -2.266911751 + 1.5 Combine like terms: -2.266911751 + 1.5 = -0.766911751 x = -0.766911751 Simplifying x = -0.766911751

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.766911751, -0.766911751}

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