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Simplifying -6 + 3x + -9x2 = -16 Solving -6 + 3x + -9x2 = -16 Solving for variable 'x'. Reorder the terms: -6 + 16 + 3x + -9x2 = -16 + 16 Combine like terms: -6 + 16 = 10 10 + 3x + -9x2 = -16 + 16 Combine like terms: -16 + 16 = 0 10 + 3x + -9x2 = 0 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 = 1.2338540397Subproblem 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 = -0.9005207063Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2338540397, -0.9005207063}
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