9x^2-3x-10=0

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Solution for 9x^2-3x-10=0 equation:


Simplifying
9x2 + -3x + -10 = 0

Reorder the terms:
-10 + -3x + 9x2 = 0

Solving
-10 + -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'.
-1.111111111 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + -0.3333333333x + 1.111111111 + x2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + -0.3333333333x + x2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + -0.3333333333x + x2 = 0 + 1.111111111
-0.3333333333x + x2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
-0.3333333333x + x2 = 1.111111111

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 = 1.111111111 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 1.111111111 + 0.02777777779

Combine like terms: 1.111111111 + 0.02777777779 = 1.13888888879
0.02777777779 + -0.3333333333x + x2 = 1.13888888879

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 1.13888888879

Calculate the square root of the right side: 1.067187373

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 1.067187373 and -1.067187373.

Subproblem 1

x + -0.1666666667 = 1.067187373 Simplifying x + -0.1666666667 = 1.067187373 Reorder the terms: -0.1666666667 + x = 1.067187373 Solving -0.1666666667 + x = 1.067187373 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 = 1.067187373 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 1.067187373 + 0.1666666667 x = 1.067187373 + 0.1666666667 Combine like terms: 1.067187373 + 0.1666666667 = 1.2338540397 x = 1.2338540397 Simplifying x = 1.2338540397

Subproblem 2

x + -0.1666666667 = -1.067187373 Simplifying x + -0.1666666667 = -1.067187373 Reorder the terms: -0.1666666667 + x = -1.067187373 Solving -0.1666666667 + x = -1.067187373 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 = -1.067187373 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -1.067187373 + 0.1666666667 x = -1.067187373 + 0.1666666667 Combine like terms: -1.067187373 + 0.1666666667 = -0.9005207063 x = -0.9005207063 Simplifying x = -0.9005207063

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2338540397, -0.9005207063}

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