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Simplifying 12x2 + 9x + -2 = 17 Reorder the terms: -2 + 9x + 12x2 = 17 Solving -2 + 9x + 12x2 = 17 Solving for variable 'x'. Reorder the terms: -2 + -17 + 9x + 12x2 = 17 + -17 Combine like terms: -2 + -17 = -19 -19 + 9x + 12x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -19 + 9x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.583333333 + 0.75x + x2 = 0 Move the constant term to the right: Add '1.583333333' to each side of the equation. -1.583333333 + 0.75x + 1.583333333 + x2 = 0 + 1.583333333 Reorder the terms: -1.583333333 + 1.583333333 + 0.75x + x2 = 0 + 1.583333333 Combine like terms: -1.583333333 + 1.583333333 = 0.000000000 0.000000000 + 0.75x + x2 = 0 + 1.583333333 0.75x + x2 = 0 + 1.583333333 Combine like terms: 0 + 1.583333333 = 1.583333333 0.75x + x2 = 1.583333333 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 1.583333333 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 1.583333333 + 0.140625 Combine like terms: 1.583333333 + 0.140625 = 1.723958333 0.140625 + 0.75x + x2 = 1.723958333 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 1.723958333 Calculate the square root of the right side: 1.312995938 Break this problem into two subproblems by setting (x + 0.375) equal to 1.312995938 and -1.312995938.Subproblem 1
x + 0.375 = 1.312995938 Simplifying x + 0.375 = 1.312995938 Reorder the terms: 0.375 + x = 1.312995938 Solving 0.375 + x = 1.312995938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 1.312995938 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.312995938 + -0.375 x = 1.312995938 + -0.375 Combine like terms: 1.312995938 + -0.375 = 0.937995938 x = 0.937995938 Simplifying x = 0.937995938Subproblem 2
x + 0.375 = -1.312995938 Simplifying x + 0.375 = -1.312995938 Reorder the terms: 0.375 + x = -1.312995938 Solving 0.375 + x = -1.312995938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -1.312995938 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.312995938 + -0.375 x = -1.312995938 + -0.375 Combine like terms: -1.312995938 + -0.375 = -1.687995938 x = -1.687995938 Simplifying x = -1.687995938Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.937995938, -1.687995938}
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