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Simplifying 17x2 + -6x + -83 = 0 Reorder the terms: -83 + -6x + 17x2 = 0 Solving -83 + -6x + 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'. -4.882352941 + -0.3529411765x + x2 = 0 Move the constant term to the right: Add '4.882352941' to each side of the equation. -4.882352941 + -0.3529411765x + 4.882352941 + x2 = 0 + 4.882352941 Reorder the terms: -4.882352941 + 4.882352941 + -0.3529411765x + x2 = 0 + 4.882352941 Combine like terms: -4.882352941 + 4.882352941 = 0.000000000 0.000000000 + -0.3529411765x + x2 = 0 + 4.882352941 -0.3529411765x + x2 = 0 + 4.882352941 Combine like terms: 0 + 4.882352941 = 4.882352941 -0.3529411765x + x2 = 4.882352941 The x term is -0.3529411765x. Take half its coefficient (-0.1764705883). Square it (0.03114186853) and add it to both sides. Add '0.03114186853' to each side of the equation. -0.3529411765x + 0.03114186853 + x2 = 4.882352941 + 0.03114186853 Reorder the terms: 0.03114186853 + -0.3529411765x + x2 = 4.882352941 + 0.03114186853 Combine like terms: 4.882352941 + 0.03114186853 = 4.91349480953 0.03114186853 + -0.3529411765x + x2 = 4.91349480953 Factor a perfect square on the left side: (x + -0.1764705883)(x + -0.1764705883) = 4.91349480953 Calculate the square root of the right side: 2.216640433 Break this problem into two subproblems by setting (x + -0.1764705883) equal to 2.216640433 and -2.216640433.Subproblem 1
x + -0.1764705883 = 2.216640433 Simplifying x + -0.1764705883 = 2.216640433 Reorder the terms: -0.1764705883 + x = 2.216640433 Solving -0.1764705883 + x = 2.216640433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1764705883' to each side of the equation. -0.1764705883 + 0.1764705883 + x = 2.216640433 + 0.1764705883 Combine like terms: -0.1764705883 + 0.1764705883 = 0.0000000000 0.0000000000 + x = 2.216640433 + 0.1764705883 x = 2.216640433 + 0.1764705883 Combine like terms: 2.216640433 + 0.1764705883 = 2.3931110213 x = 2.3931110213 Simplifying x = 2.3931110213Subproblem 2
x + -0.1764705883 = -2.216640433 Simplifying x + -0.1764705883 = -2.216640433 Reorder the terms: -0.1764705883 + x = -2.216640433 Solving -0.1764705883 + x = -2.216640433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1764705883' to each side of the equation. -0.1764705883 + 0.1764705883 + x = -2.216640433 + 0.1764705883 Combine like terms: -0.1764705883 + 0.1764705883 = 0.0000000000 0.0000000000 + x = -2.216640433 + 0.1764705883 x = -2.216640433 + 0.1764705883 Combine like terms: -2.216640433 + 0.1764705883 = -2.0401698447 x = -2.0401698447 Simplifying x = -2.0401698447Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3931110213, -2.0401698447}
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