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Simplifying 12x2 + -17x + -9 = 0 Reorder the terms: -9 + -17x + 12x2 = 0 Solving -9 + -17x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.75 + -1.416666667x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.416666667x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.416666667x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.416666667x + x2 = 0 + 0.75 -1.416666667x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.416666667x + x2 = 0.75 The x term is -1.416666667x. Take half its coefficient (-0.7083333335). Square it (0.5017361113) and add it to both sides. Add '0.5017361113' to each side of the equation. -1.416666667x + 0.5017361113 + x2 = 0.75 + 0.5017361113 Reorder the terms: 0.5017361113 + -1.416666667x + x2 = 0.75 + 0.5017361113 Combine like terms: 0.75 + 0.5017361113 = 1.2517361113 0.5017361113 + -1.416666667x + x2 = 1.2517361113 Factor a perfect square on the left side: (x + -0.7083333335)(x + -0.7083333335) = 1.2517361113 Calculate the square root of the right side: 1.118810132 Break this problem into two subproblems by setting (x + -0.7083333335) equal to 1.118810132 and -1.118810132.Subproblem 1
x + -0.7083333335 = 1.118810132 Simplifying x + -0.7083333335 = 1.118810132 Reorder the terms: -0.7083333335 + x = 1.118810132 Solving -0.7083333335 + x = 1.118810132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + x = 1.118810132 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + x = 1.118810132 + 0.7083333335 x = 1.118810132 + 0.7083333335 Combine like terms: 1.118810132 + 0.7083333335 = 1.8271434655 x = 1.8271434655 Simplifying x = 1.8271434655Subproblem 2
x + -0.7083333335 = -1.118810132 Simplifying x + -0.7083333335 = -1.118810132 Reorder the terms: -0.7083333335 + x = -1.118810132 Solving -0.7083333335 + x = -1.118810132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + x = -1.118810132 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + x = -1.118810132 + 0.7083333335 x = -1.118810132 + 0.7083333335 Combine like terms: -1.118810132 + 0.7083333335 = -0.4104767985 x = -0.4104767985 Simplifying x = -0.4104767985Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8271434655, -0.4104767985}
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