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Simplifying (2x2 + -6x) + -1(3x + -3x2 + 8x + 2) = 0 Reorder the terms: (-6x + 2x2) + -1(3x + -3x2 + 8x + 2) = 0 Remove parenthesis around (-6x + 2x2) -6x + 2x2 + -1(3x + -3x2 + 8x + 2) = 0 Reorder the terms: -6x + 2x2 + -1(2 + 3x + 8x + -3x2) = 0 Combine like terms: 3x + 8x = 11x -6x + 2x2 + -1(2 + 11x + -3x2) = 0 -6x + 2x2 + (2 * -1 + 11x * -1 + -3x2 * -1) = 0 -6x + 2x2 + (-2 + -11x + 3x2) = 0 Reorder the terms: -2 + -6x + -11x + 2x2 + 3x2 = 0 Combine like terms: -6x + -11x = -17x -2 + -17x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 -2 + -17x + 5x2 = 0 Solving -2 + -17x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -3.4x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -3.4x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -3.4x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -3.4x + x2 = 0 + 0.4 -3.4x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -3.4x + x2 = 0.4 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = 0.4 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 0.4 + 2.89 Combine like terms: 0.4 + 2.89 = 3.29 2.89 + -3.4x + x2 = 3.29 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 3.29 Calculate the square root of the right side: 1.813835715 Break this problem into two subproblems by setting (x + -1.7) equal to 1.813835715 and -1.813835715.Subproblem 1
x + -1.7 = 1.813835715 Simplifying x + -1.7 = 1.813835715 Reorder the terms: -1.7 + x = 1.813835715 Solving -1.7 + x = 1.813835715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 1.813835715 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 1.813835715 + 1.7 x = 1.813835715 + 1.7 Combine like terms: 1.813835715 + 1.7 = 3.513835715 x = 3.513835715 Simplifying x = 3.513835715Subproblem 2
x + -1.7 = -1.813835715 Simplifying x + -1.7 = -1.813835715 Reorder the terms: -1.7 + x = -1.813835715 Solving -1.7 + x = -1.813835715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -1.813835715 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -1.813835715 + 1.7 x = -1.813835715 + 1.7 Combine like terms: -1.813835715 + 1.7 = -0.113835715 x = -0.113835715 Simplifying x = -0.113835715Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.513835715, -0.113835715}
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