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Simplifying 17x2 + 5x + -3 = 0 Reorder the terms: -3 + 5x + 17x2 = 0 Solving -3 + 5x + 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'. -0.1764705882 + 0.2941176471x + x2 = 0 Move the constant term to the right: Add '0.1764705882' to each side of the equation. -0.1764705882 + 0.2941176471x + 0.1764705882 + x2 = 0 + 0.1764705882 Reorder the terms: -0.1764705882 + 0.1764705882 + 0.2941176471x + x2 = 0 + 0.1764705882 Combine like terms: -0.1764705882 + 0.1764705882 = 0.0000000000 0.0000000000 + 0.2941176471x + x2 = 0 + 0.1764705882 0.2941176471x + x2 = 0 + 0.1764705882 Combine like terms: 0 + 0.1764705882 = 0.1764705882 0.2941176471x + x2 = 0.1764705882 The x term is 0.2941176471x. Take half its coefficient (0.1470588236). Square it (0.02162629760) and add it to both sides. Add '0.02162629760' to each side of the equation. 0.2941176471x + 0.02162629760 + x2 = 0.1764705882 + 0.02162629760 Reorder the terms: 0.02162629760 + 0.2941176471x + x2 = 0.1764705882 + 0.02162629760 Combine like terms: 0.1764705882 + 0.02162629760 = 0.1980968858 0.02162629760 + 0.2941176471x + x2 = 0.1980968858 Factor a perfect square on the left side: (x + 0.1470588236)(x + 0.1470588236) = 0.1980968858 Calculate the square root of the right side: 0.445080763 Break this problem into two subproblems by setting (x + 0.1470588236) equal to 0.445080763 and -0.445080763.Subproblem 1
x + 0.1470588236 = 0.445080763 Simplifying x + 0.1470588236 = 0.445080763 Reorder the terms: 0.1470588236 + x = 0.445080763 Solving 0.1470588236 + x = 0.445080763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1470588236' to each side of the equation. 0.1470588236 + -0.1470588236 + x = 0.445080763 + -0.1470588236 Combine like terms: 0.1470588236 + -0.1470588236 = 0.0000000000 0.0000000000 + x = 0.445080763 + -0.1470588236 x = 0.445080763 + -0.1470588236 Combine like terms: 0.445080763 + -0.1470588236 = 0.2980219394 x = 0.2980219394 Simplifying x = 0.2980219394Subproblem 2
x + 0.1470588236 = -0.445080763 Simplifying x + 0.1470588236 = -0.445080763 Reorder the terms: 0.1470588236 + x = -0.445080763 Solving 0.1470588236 + x = -0.445080763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1470588236' to each side of the equation. 0.1470588236 + -0.1470588236 + x = -0.445080763 + -0.1470588236 Combine like terms: 0.1470588236 + -0.1470588236 = 0.0000000000 0.0000000000 + x = -0.445080763 + -0.1470588236 x = -0.445080763 + -0.1470588236 Combine like terms: -0.445080763 + -0.1470588236 = -0.5921395866 x = -0.5921395866 Simplifying x = -0.5921395866Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2980219394, -0.5921395866}
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