9x^2+13x-73=0

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Solution for 9x^2+13x-73=0 equation:


Simplifying
9x2 + 13x + -73 = 0

Reorder the terms:
-73 + 13x + 9x2 = 0

Solving
-73 + 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'.
-8.111111111 + 1.444444444x + x2 = 0

Move the constant term to the right:

Add '8.111111111' to each side of the equation.
-8.111111111 + 1.444444444x + 8.111111111 + x2 = 0 + 8.111111111

Reorder the terms:
-8.111111111 + 8.111111111 + 1.444444444x + x2 = 0 + 8.111111111

Combine like terms: -8.111111111 + 8.111111111 = 0.000000000
0.000000000 + 1.444444444x + x2 = 0 + 8.111111111
1.444444444x + x2 = 0 + 8.111111111

Combine like terms: 0 + 8.111111111 = 8.111111111
1.444444444x + x2 = 8.111111111

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 = 8.111111111 + 0.5216049380

Reorder the terms:
0.5216049380 + 1.444444444x + x2 = 8.111111111 + 0.5216049380

Combine like terms: 8.111111111 + 0.5216049380 = 8.632716049
0.5216049380 + 1.444444444x + x2 = 8.632716049

Factor a perfect square on the left side:
(x + 0.722222222)(x + 0.722222222) = 8.632716049

Calculate the square root of the right side: 2.938148405

Break this problem into two subproblems by setting 
(x + 0.722222222) equal to 2.938148405 and -2.938148405.

Subproblem 1

x + 0.722222222 = 2.938148405 Simplifying x + 0.722222222 = 2.938148405 Reorder the terms: 0.722222222 + x = 2.938148405 Solving 0.722222222 + x = 2.938148405 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 = 2.938148405 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = 2.938148405 + -0.722222222 x = 2.938148405 + -0.722222222 Combine like terms: 2.938148405 + -0.722222222 = 2.215926183 x = 2.215926183 Simplifying x = 2.215926183

Subproblem 2

x + 0.722222222 = -2.938148405 Simplifying x + 0.722222222 = -2.938148405 Reorder the terms: 0.722222222 + x = -2.938148405 Solving 0.722222222 + x = -2.938148405 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 = -2.938148405 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = -2.938148405 + -0.722222222 x = -2.938148405 + -0.722222222 Combine like terms: -2.938148405 + -0.722222222 = -3.660370627 x = -3.660370627 Simplifying x = -3.660370627

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.215926183, -3.660370627}

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