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Simplifying 17x2 + 3x + -13 = 0 Reorder the terms: -13 + 3x + 17x2 = 0 Solving -13 + 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'. -0.7647058824 + 0.1764705882x + x2 = 0 Move the constant term to the right: Add '0.7647058824' to each side of the equation. -0.7647058824 + 0.1764705882x + 0.7647058824 + x2 = 0 + 0.7647058824 Reorder the terms: -0.7647058824 + 0.7647058824 + 0.1764705882x + x2 = 0 + 0.7647058824 Combine like terms: -0.7647058824 + 0.7647058824 = 0.0000000000 0.0000000000 + 0.1764705882x + x2 = 0 + 0.7647058824 0.1764705882x + x2 = 0 + 0.7647058824 Combine like terms: 0 + 0.7647058824 = 0.7647058824 0.1764705882x + x2 = 0.7647058824 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 = 0.7647058824 + 0.007785467125 Reorder the terms: 0.007785467125 + 0.1764705882x + x2 = 0.7647058824 + 0.007785467125 Combine like terms: 0.7647058824 + 0.007785467125 = 0.772491349525 0.007785467125 + 0.1764705882x + x2 = 0.772491349525 Factor a perfect square on the left side: (x + 0.0882352941)(x + 0.0882352941) = 0.772491349525 Calculate the square root of the right side: 0.87891487 Break this problem into two subproblems by setting (x + 0.0882352941) equal to 0.87891487 and -0.87891487.Subproblem 1
x + 0.0882352941 = 0.87891487 Simplifying x + 0.0882352941 = 0.87891487 Reorder the terms: 0.0882352941 + x = 0.87891487 Solving 0.0882352941 + x = 0.87891487 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 = 0.87891487 + -0.0882352941 Combine like terms: 0.0882352941 + -0.0882352941 = 0.0000000000 0.0000000000 + x = 0.87891487 + -0.0882352941 x = 0.87891487 + -0.0882352941 Combine like terms: 0.87891487 + -0.0882352941 = 0.7906795759 x = 0.7906795759 Simplifying x = 0.7906795759Subproblem 2
x + 0.0882352941 = -0.87891487 Simplifying x + 0.0882352941 = -0.87891487 Reorder the terms: 0.0882352941 + x = -0.87891487 Solving 0.0882352941 + x = -0.87891487 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 = -0.87891487 + -0.0882352941 Combine like terms: 0.0882352941 + -0.0882352941 = 0.0000000000 0.0000000000 + x = -0.87891487 + -0.0882352941 x = -0.87891487 + -0.0882352941 Combine like terms: -0.87891487 + -0.0882352941 = -0.9671501641 x = -0.9671501641 Simplifying x = -0.9671501641Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7906795759, -0.9671501641}
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