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Simplifying (3x2 + -6x + 1) + -1(8x2 + 5x + -3) + -1(9x2 + 9x + -9) + (3x2 + 5x + 2) = 0 Reorder the terms: (1 + -6x + 3x2) + -1(8x2 + 5x + -3) + -1(9x2 + 9x + -9) + (3x2 + 5x + 2) = 0 Remove parenthesis around (1 + -6x + 3x2) 1 + -6x + 3x2 + -1(8x2 + 5x + -3) + -1(9x2 + 9x + -9) + (3x2 + 5x + 2) = 0 Reorder the terms: 1 + -6x + 3x2 + -1(-3 + 5x + 8x2) + -1(9x2 + 9x + -9) + (3x2 + 5x + 2) = 0 1 + -6x + 3x2 + (-3 * -1 + 5x * -1 + 8x2 * -1) + -1(9x2 + 9x + -9) + (3x2 + 5x + 2) = 0 1 + -6x + 3x2 + (3 + -5x + -8x2) + -1(9x2 + 9x + -9) + (3x2 + 5x + 2) = 0 Reorder the terms: 1 + -6x + 3x2 + 3 + -5x + -8x2 + -1(-9 + 9x + 9x2) + (3x2 + 5x + 2) = 0 1 + -6x + 3x2 + 3 + -5x + -8x2 + (-9 * -1 + 9x * -1 + 9x2 * -1) + (3x2 + 5x + 2) = 0 1 + -6x + 3x2 + 3 + -5x + -8x2 + (9 + -9x + -9x2) + (3x2 + 5x + 2) = 0 Reorder the terms: 1 + -6x + 3x2 + 3 + -5x + -8x2 + 9 + -9x + -9x2 + (2 + 5x + 3x2) = 0 Remove parenthesis around (2 + 5x + 3x2) 1 + -6x + 3x2 + 3 + -5x + -8x2 + 9 + -9x + -9x2 + 2 + 5x + 3x2 = 0 Reorder the terms: 1 + 3 + 9 + 2 + -6x + -5x + -9x + 5x + 3x2 + -8x2 + -9x2 + 3x2 = 0 Combine like terms: 1 + 3 = 4 4 + 9 + 2 + -6x + -5x + -9x + 5x + 3x2 + -8x2 + -9x2 + 3x2 = 0 Combine like terms: 4 + 9 = 13 13 + 2 + -6x + -5x + -9x + 5x + 3x2 + -8x2 + -9x2 + 3x2 = 0 Combine like terms: 13 + 2 = 15 15 + -6x + -5x + -9x + 5x + 3x2 + -8x2 + -9x2 + 3x2 = 0 Combine like terms: -6x + -5x = -11x 15 + -11x + -9x + 5x + 3x2 + -8x2 + -9x2 + 3x2 = 0 Combine like terms: -11x + -9x = -20x 15 + -20x + 5x + 3x2 + -8x2 + -9x2 + 3x2 = 0 Combine like terms: -20x + 5x = -15x 15 + -15x + 3x2 + -8x2 + -9x2 + 3x2 = 0 Combine like terms: 3x2 + -8x2 = -5x2 15 + -15x + -5x2 + -9x2 + 3x2 = 0 Combine like terms: -5x2 + -9x2 = -14x2 15 + -15x + -14x2 + 3x2 = 0 Combine like terms: -14x2 + 3x2 = -11x2 15 + -15x + -11x2 = 0 Solving 15 + -15x + -11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -1.363636364 + 1.363636364x + x2 = 0 Move the constant term to the right: Add '1.363636364' to each side of the equation. -1.363636364 + 1.363636364x + 1.363636364 + x2 = 0 + 1.363636364 Reorder the terms: -1.363636364 + 1.363636364 + 1.363636364x + x2 = 0 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + 1.363636364x + x2 = 0 + 1.363636364 1.363636364x + x2 = 0 + 1.363636364 Combine like terms: 0 + 1.363636364 = 1.363636364 1.363636364x + x2 = 1.363636364 The x term is 1.363636364x. Take half its coefficient (0.681818182). Square it (0.4648760333) and add it to both sides. Add '0.4648760333' to each side of the equation. 1.363636364x + 0.4648760333 + x2 = 1.363636364 + 0.4648760333 Reorder the terms: 0.4648760333 + 1.363636364x + x2 = 1.363636364 + 0.4648760333 Combine like terms: 1.363636364 + 0.4648760333 = 1.8285123973 0.4648760333 + 1.363636364x + x2 = 1.8285123973 Factor a perfect square on the left side: (x + 0.681818182)(x + 0.681818182) = 1.8285123973 Calculate the square root of the right side: 1.35222498 Break this problem into two subproblems by setting (x + 0.681818182) equal to 1.35222498 and -1.35222498.Subproblem 1
x + 0.681818182 = 1.35222498 Simplifying x + 0.681818182 = 1.35222498 Reorder the terms: 0.681818182 + x = 1.35222498 Solving 0.681818182 + x = 1.35222498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.681818182' to each side of the equation. 0.681818182 + -0.681818182 + x = 1.35222498 + -0.681818182 Combine like terms: 0.681818182 + -0.681818182 = 0.000000000 0.000000000 + x = 1.35222498 + -0.681818182 x = 1.35222498 + -0.681818182 Combine like terms: 1.35222498 + -0.681818182 = 0.670406798 x = 0.670406798 Simplifying x = 0.670406798Subproblem 2
x + 0.681818182 = -1.35222498 Simplifying x + 0.681818182 = -1.35222498 Reorder the terms: 0.681818182 + x = -1.35222498 Solving 0.681818182 + x = -1.35222498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.681818182' to each side of the equation. 0.681818182 + -0.681818182 + x = -1.35222498 + -0.681818182 Combine like terms: 0.681818182 + -0.681818182 = 0.000000000 0.000000000 + x = -1.35222498 + -0.681818182 x = -1.35222498 + -0.681818182 Combine like terms: -1.35222498 + -0.681818182 = -2.034043162 x = -2.034043162 Simplifying x = -2.034043162Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.670406798, -2.034043162}
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