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Simplifying 9x2 = 30x + -17 Reorder the terms: 9x2 = -17 + 30x Solving 9x2 = -17 + 30x Solving for variable 'x'. Reorder the terms: 17 + -30x + 9x2 = -17 + 30x + 17 + -30x Reorder the terms: 17 + -30x + 9x2 = -17 + 17 + 30x + -30x Combine like terms: -17 + 17 = 0 17 + -30x + 9x2 = 0 + 30x + -30x 17 + -30x + 9x2 = 30x + -30x Combine like terms: 30x + -30x = 0 17 + -30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.888888889 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-1.888888889' to each side of the equation. 1.888888889 + -3.333333333x + -1.888888889 + x2 = 0 + -1.888888889 Reorder the terms: 1.888888889 + -1.888888889 + -3.333333333x + x2 = 0 + -1.888888889 Combine like terms: 1.888888889 + -1.888888889 = 0.000000000 0.000000000 + -3.333333333x + x2 = 0 + -1.888888889 -3.333333333x + x2 = 0 + -1.888888889 Combine like terms: 0 + -1.888888889 = -1.888888889 -3.333333333x + x2 = -1.888888889 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = -1.888888889 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -1.888888889 + 2.777777779 Combine like terms: -1.888888889 + 2.777777779 = 0.88888889 2.777777779 + -3.333333333x + x2 = 0.88888889 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 0.88888889 Calculate the square root of the right side: 0.942809042 Break this problem into two subproblems by setting (x + -1.666666667) equal to 0.942809042 and -0.942809042.Subproblem 1
x + -1.666666667 = 0.942809042 Simplifying x + -1.666666667 = 0.942809042 Reorder the terms: -1.666666667 + x = 0.942809042 Solving -1.666666667 + x = 0.942809042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 0.942809042 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 0.942809042 + 1.666666667 x = 0.942809042 + 1.666666667 Combine like terms: 0.942809042 + 1.666666667 = 2.609475709 x = 2.609475709 Simplifying x = 2.609475709Subproblem 2
x + -1.666666667 = -0.942809042 Simplifying x + -1.666666667 = -0.942809042 Reorder the terms: -1.666666667 + x = -0.942809042 Solving -1.666666667 + x = -0.942809042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -0.942809042 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -0.942809042 + 1.666666667 x = -0.942809042 + 1.666666667 Combine like terms: -0.942809042 + 1.666666667 = 0.723857625 x = 0.723857625 Simplifying x = 0.723857625Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.609475709, 0.723857625}
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