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Simplifying 17x2 + -6x + -28 = 0 Reorder the terms: -28 + -6x + 17x2 = 0 Solving -28 + -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'. -1.647058824 + -0.3529411765x + x2 = 0 Move the constant term to the right: Add '1.647058824' to each side of the equation. -1.647058824 + -0.3529411765x + 1.647058824 + x2 = 0 + 1.647058824 Reorder the terms: -1.647058824 + 1.647058824 + -0.3529411765x + x2 = 0 + 1.647058824 Combine like terms: -1.647058824 + 1.647058824 = 0.000000000 0.000000000 + -0.3529411765x + x2 = 0 + 1.647058824 -0.3529411765x + x2 = 0 + 1.647058824 Combine like terms: 0 + 1.647058824 = 1.647058824 -0.3529411765x + x2 = 1.647058824 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 = 1.647058824 + 0.03114186853 Reorder the terms: 0.03114186853 + -0.3529411765x + x2 = 1.647058824 + 0.03114186853 Combine like terms: 1.647058824 + 0.03114186853 = 1.67820069253 0.03114186853 + -0.3529411765x + x2 = 1.67820069253 Factor a perfect square on the left side: (x + -0.1764705883)(x + -0.1764705883) = 1.67820069253 Calculate the square root of the right side: 1.295453856 Break this problem into two subproblems by setting (x + -0.1764705883) equal to 1.295453856 and -1.295453856.Subproblem 1
x + -0.1764705883 = 1.295453856 Simplifying x + -0.1764705883 = 1.295453856 Reorder the terms: -0.1764705883 + x = 1.295453856 Solving -0.1764705883 + x = 1.295453856 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 = 1.295453856 + 0.1764705883 Combine like terms: -0.1764705883 + 0.1764705883 = 0.0000000000 0.0000000000 + x = 1.295453856 + 0.1764705883 x = 1.295453856 + 0.1764705883 Combine like terms: 1.295453856 + 0.1764705883 = 1.4719244443 x = 1.4719244443 Simplifying x = 1.4719244443Subproblem 2
x + -0.1764705883 = -1.295453856 Simplifying x + -0.1764705883 = -1.295453856 Reorder the terms: -0.1764705883 + x = -1.295453856 Solving -0.1764705883 + x = -1.295453856 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 = -1.295453856 + 0.1764705883 Combine like terms: -0.1764705883 + 0.1764705883 = 0.0000000000 0.0000000000 + x = -1.295453856 + 0.1764705883 x = -1.295453856 + 0.1764705883 Combine like terms: -1.295453856 + 0.1764705883 = -1.1189832677 x = -1.1189832677 Simplifying x = -1.1189832677Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4719244443, -1.1189832677}
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