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Simplifying 17x2 + -30x + 8 = 0 Reorder the terms: 8 + -30x + 17x2 = 0 Solving 8 + -30x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 0.4705882353 + -1.764705882x + x2 = 0 Move the constant term to the right: Add '-0.4705882353' to each side of the equation. 0.4705882353 + -1.764705882x + -0.4705882353 + x2 = 0 + -0.4705882353 Reorder the terms: 0.4705882353 + -0.4705882353 + -1.764705882x + x2 = 0 + -0.4705882353 Combine like terms: 0.4705882353 + -0.4705882353 = 0.0000000000 0.0000000000 + -1.764705882x + x2 = 0 + -0.4705882353 -1.764705882x + x2 = 0 + -0.4705882353 Combine like terms: 0 + -0.4705882353 = -0.4705882353 -1.764705882x + x2 = -0.4705882353 The x term is -1.764705882x. Take half its coefficient (-0.882352941). Square it (0.7785467125) and add it to both sides. Add '0.7785467125' to each side of the equation. -1.764705882x + 0.7785467125 + x2 = -0.4705882353 + 0.7785467125 Reorder the terms: 0.7785467125 + -1.764705882x + x2 = -0.4705882353 + 0.7785467125 Combine like terms: -0.4705882353 + 0.7785467125 = 0.3079584772 0.7785467125 + -1.764705882x + x2 = 0.3079584772 Factor a perfect square on the left side: (x + -0.882352941)(x + -0.882352941) = 0.3079584772 Calculate the square root of the right side: 0.554940066 Break this problem into two subproblems by setting (x + -0.882352941) equal to 0.554940066 and -0.554940066.Subproblem 1
x + -0.882352941 = 0.554940066 Simplifying x + -0.882352941 = 0.554940066 Reorder the terms: -0.882352941 + x = 0.554940066 Solving -0.882352941 + x = 0.554940066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.882352941' to each side of the equation. -0.882352941 + 0.882352941 + x = 0.554940066 + 0.882352941 Combine like terms: -0.882352941 + 0.882352941 = 0.000000000 0.000000000 + x = 0.554940066 + 0.882352941 x = 0.554940066 + 0.882352941 Combine like terms: 0.554940066 + 0.882352941 = 1.437293007 x = 1.437293007 Simplifying x = 1.437293007Subproblem 2
x + -0.882352941 = -0.554940066 Simplifying x + -0.882352941 = -0.554940066 Reorder the terms: -0.882352941 + x = -0.554940066 Solving -0.882352941 + x = -0.554940066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.882352941' to each side of the equation. -0.882352941 + 0.882352941 + x = -0.554940066 + 0.882352941 Combine like terms: -0.882352941 + 0.882352941 = 0.000000000 0.000000000 + x = -0.554940066 + 0.882352941 x = -0.554940066 + 0.882352941 Combine like terms: -0.554940066 + 0.882352941 = 0.327412875 x = 0.327412875 Simplifying x = 0.327412875Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.437293007, 0.327412875}
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