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Simplifying 9 + -6x + x2 = (27 + -9x + -3x2) * 1 Reorder the terms for easier multiplication: 9 + -6x + x2 = 1(27 + -9x + -3x2) 9 + -6x + x2 = (27 * 1 + -9x * 1 + -3x2 * 1) 9 + -6x + x2 = (27 + -9x + -3x2) Solving 9 + -6x + x2 = 27 + -9x + -3x2 Solving for variable 'x'. Reorder the terms: 9 + -27 + -6x + 9x + x2 + 3x2 = 27 + -9x + -3x2 + -27 + 9x + 3x2 Combine like terms: 9 + -27 = -18 -18 + -6x + 9x + x2 + 3x2 = 27 + -9x + -3x2 + -27 + 9x + 3x2 Combine like terms: -6x + 9x = 3x -18 + 3x + x2 + 3x2 = 27 + -9x + -3x2 + -27 + 9x + 3x2 Combine like terms: x2 + 3x2 = 4x2 -18 + 3x + 4x2 = 27 + -9x + -3x2 + -27 + 9x + 3x2 Reorder the terms: -18 + 3x + 4x2 = 27 + -27 + -9x + 9x + -3x2 + 3x2 Combine like terms: 27 + -27 = 0 -18 + 3x + 4x2 = 0 + -9x + 9x + -3x2 + 3x2 -18 + 3x + 4x2 = -9x + 9x + -3x2 + 3x2 Combine like terms: -9x + 9x = 0 -18 + 3x + 4x2 = 0 + -3x2 + 3x2 -18 + 3x + 4x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -18 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + 0.75x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 0.75x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 0.75x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 0.75x + x2 = 0 + 4.5 0.75x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 0.75x + x2 = 4.5 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 = 4.5 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 4.5 + 0.140625 Combine like terms: 4.5 + 0.140625 = 4.640625 0.140625 + 0.75x + x2 = 4.640625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 4.640625 Calculate the square root of the right side: 2.154210992 Break this problem into two subproblems by setting (x + 0.375) equal to 2.154210992 and -2.154210992.Subproblem 1
x + 0.375 = 2.154210992 Simplifying x + 0.375 = 2.154210992 Reorder the terms: 0.375 + x = 2.154210992 Solving 0.375 + x = 2.154210992 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 = 2.154210992 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 2.154210992 + -0.375 x = 2.154210992 + -0.375 Combine like terms: 2.154210992 + -0.375 = 1.779210992 x = 1.779210992 Simplifying x = 1.779210992Subproblem 2
x + 0.375 = -2.154210992 Simplifying x + 0.375 = -2.154210992 Reorder the terms: 0.375 + x = -2.154210992 Solving 0.375 + x = -2.154210992 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 = -2.154210992 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -2.154210992 + -0.375 x = -2.154210992 + -0.375 Combine like terms: -2.154210992 + -0.375 = -2.529210992 x = -2.529210992 Simplifying x = -2.529210992Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.779210992, -2.529210992}
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