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Simplifying (2x + -5)(3x + 2) + -1(x2 + -3x + -8) = 0 Reorder the terms: (-5 + 2x)(3x + 2) + -1(x2 + -3x + -8) = 0 Reorder the terms: (-5 + 2x)(2 + 3x) + -1(x2 + -3x + -8) = 0 Multiply (-5 + 2x) * (2 + 3x) (-5(2 + 3x) + 2x * (2 + 3x)) + -1(x2 + -3x + -8) = 0 ((2 * -5 + 3x * -5) + 2x * (2 + 3x)) + -1(x2 + -3x + -8) = 0 ((-10 + -15x) + 2x * (2 + 3x)) + -1(x2 + -3x + -8) = 0 (-10 + -15x + (2 * 2x + 3x * 2x)) + -1(x2 + -3x + -8) = 0 (-10 + -15x + (4x + 6x2)) + -1(x2 + -3x + -8) = 0 Combine like terms: -15x + 4x = -11x (-10 + -11x + 6x2) + -1(x2 + -3x + -8) = 0 Reorder the terms: -10 + -11x + 6x2 + -1(-8 + -3x + x2) = 0 -10 + -11x + 6x2 + (-8 * -1 + -3x * -1 + x2 * -1) = 0 -10 + -11x + 6x2 + (8 + 3x + -1x2) = 0 Reorder the terms: -10 + 8 + -11x + 3x + 6x2 + -1x2 = 0 Combine like terms: -10 + 8 = -2 -2 + -11x + 3x + 6x2 + -1x2 = 0 Combine like terms: -11x + 3x = -8x -2 + -8x + 6x2 + -1x2 = 0 Combine like terms: 6x2 + -1x2 = 5x2 -2 + -8x + 5x2 = 0 Solving -2 + -8x + 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 + -1.6x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.6x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.6x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.6x + x2 = 0 + 0.4 -1.6x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -1.6x + x2 = 0.4 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 0.4 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 0.4 + 0.64 Combine like terms: 0.4 + 0.64 = 1.04 0.64 + -1.6x + x2 = 1.04 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 1.04 Calculate the square root of the right side: 1.019803903 Break this problem into two subproblems by setting (x + -0.8) equal to 1.019803903 and -1.019803903.Subproblem 1
x + -0.8 = 1.019803903 Simplifying x + -0.8 = 1.019803903 Reorder the terms: -0.8 + x = 1.019803903 Solving -0.8 + x = 1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.019803903 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.019803903 + 0.8 x = 1.019803903 + 0.8 Combine like terms: 1.019803903 + 0.8 = 1.819803903 x = 1.819803903 Simplifying x = 1.819803903Subproblem 2
x + -0.8 = -1.019803903 Simplifying x + -0.8 = -1.019803903 Reorder the terms: -0.8 + x = -1.019803903 Solving -0.8 + x = -1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.019803903 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.019803903 + 0.8 x = -1.019803903 + 0.8 Combine like terms: -1.019803903 + 0.8 = -0.219803903 x = -0.219803903 Simplifying x = -0.219803903Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.819803903, -0.219803903}
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