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Simplifying 17x2 + 3x + -30 = 0 Reorder the terms: -30 + 3x + 17x2 = 0 Solving -30 + 3x + 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'. -1.764705882 + 0.1764705882x + x2 = 0 Move the constant term to the right: Add '1.764705882' to each side of the equation. -1.764705882 + 0.1764705882x + 1.764705882 + x2 = 0 + 1.764705882 Reorder the terms: -1.764705882 + 1.764705882 + 0.1764705882x + x2 = 0 + 1.764705882 Combine like terms: -1.764705882 + 1.764705882 = 0.000000000 0.000000000 + 0.1764705882x + x2 = 0 + 1.764705882 0.1764705882x + x2 = 0 + 1.764705882 Combine like terms: 0 + 1.764705882 = 1.764705882 0.1764705882x + x2 = 1.764705882 The x term is 0.1764705882x. Take half its coefficient (0.0882352941). Square it (0.007785467125) and add it to both sides. Add '0.007785467125' to each side of the equation. 0.1764705882x + 0.007785467125 + x2 = 1.764705882 + 0.007785467125 Reorder the terms: 0.007785467125 + 0.1764705882x + x2 = 1.764705882 + 0.007785467125 Combine like terms: 1.764705882 + 0.007785467125 = 1.772491349125 0.007785467125 + 0.1764705882x + x2 = 1.772491349125 Factor a perfect square on the left side: (x + 0.0882352941)(x + 0.0882352941) = 1.772491349125 Calculate the square root of the right side: 1.331349447 Break this problem into two subproblems by setting (x + 0.0882352941) equal to 1.331349447 and -1.331349447.Subproblem 1
x + 0.0882352941 = 1.331349447 Simplifying x + 0.0882352941 = 1.331349447 Reorder the terms: 0.0882352941 + x = 1.331349447 Solving 0.0882352941 + x = 1.331349447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0882352941' to each side of the equation. 0.0882352941 + -0.0882352941 + x = 1.331349447 + -0.0882352941 Combine like terms: 0.0882352941 + -0.0882352941 = 0.0000000000 0.0000000000 + x = 1.331349447 + -0.0882352941 x = 1.331349447 + -0.0882352941 Combine like terms: 1.331349447 + -0.0882352941 = 1.2431141529 x = 1.2431141529 Simplifying x = 1.2431141529Subproblem 2
x + 0.0882352941 = -1.331349447 Simplifying x + 0.0882352941 = -1.331349447 Reorder the terms: 0.0882352941 + x = -1.331349447 Solving 0.0882352941 + x = -1.331349447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0882352941' to each side of the equation. 0.0882352941 + -0.0882352941 + x = -1.331349447 + -0.0882352941 Combine like terms: 0.0882352941 + -0.0882352941 = 0.0000000000 0.0000000000 + x = -1.331349447 + -0.0882352941 x = -1.331349447 + -0.0882352941 Combine like terms: -1.331349447 + -0.0882352941 = -1.4195847411 x = -1.4195847411 Simplifying x = -1.4195847411Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2431141529, -1.4195847411}
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