9x^2-13x-8=0

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Solution for 9x^2-13x-8=0 equation:


Simplifying
9x2 + -13x + -8 = 0

Reorder the terms:
-8 + -13x + 9x2 = 0

Solving
-8 + -13x + 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'.
-0.8888888889 + -1.444444444x + x2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + -1.444444444x + 0.8888888889 + x2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + -1.444444444x + x2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + -1.444444444x + x2 = 0 + 0.8888888889
-1.444444444x + x2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
-1.444444444x + x2 = 0.8888888889

The x term is -1.444444444x.  Take half its coefficient (-0.722222222).
Square it (0.5216049380) and add it to both sides.

Add '0.5216049380' to each side of the equation.
-1.444444444x + 0.5216049380 + x2 = 0.8888888889 + 0.5216049380

Reorder the terms:
0.5216049380 + -1.444444444x + x2 = 0.8888888889 + 0.5216049380

Combine like terms: 0.8888888889 + 0.5216049380 = 1.4104938269
0.5216049380 + -1.444444444x + x2 = 1.4104938269

Factor a perfect square on the left side:
(x + -0.722222222)(x + -0.722222222) = 1.4104938269

Calculate the square root of the right side: 1.187642129

Break this problem into two subproblems by setting 
(x + -0.722222222) equal to 1.187642129 and -1.187642129.

Subproblem 1

x + -0.722222222 = 1.187642129 Simplifying x + -0.722222222 = 1.187642129 Reorder the terms: -0.722222222 + x = 1.187642129 Solving -0.722222222 + x = 1.187642129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = 1.187642129 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = 1.187642129 + 0.722222222 x = 1.187642129 + 0.722222222 Combine like terms: 1.187642129 + 0.722222222 = 1.909864351 x = 1.909864351 Simplifying x = 1.909864351

Subproblem 2

x + -0.722222222 = -1.187642129 Simplifying x + -0.722222222 = -1.187642129 Reorder the terms: -0.722222222 + x = -1.187642129 Solving -0.722222222 + x = -1.187642129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = -1.187642129 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = -1.187642129 + 0.722222222 x = -1.187642129 + 0.722222222 Combine like terms: -1.187642129 + 0.722222222 = -0.465419907 x = -0.465419907 Simplifying x = -0.465419907

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.909864351, -0.465419907}

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