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Simplifying 17x2 + -3x + -15 = 0 Reorder the terms: -15 + -3x + 17x2 = 0 Solving -15 + -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'. -0.8823529412 + -0.1764705882x + x2 = 0 Move the constant term to the right: Add '0.8823529412' to each side of the equation. -0.8823529412 + -0.1764705882x + 0.8823529412 + x2 = 0 + 0.8823529412 Reorder the terms: -0.8823529412 + 0.8823529412 + -0.1764705882x + x2 = 0 + 0.8823529412 Combine like terms: -0.8823529412 + 0.8823529412 = 0.0000000000 0.0000000000 + -0.1764705882x + x2 = 0 + 0.8823529412 -0.1764705882x + x2 = 0 + 0.8823529412 Combine like terms: 0 + 0.8823529412 = 0.8823529412 -0.1764705882x + x2 = 0.8823529412 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 = 0.8823529412 + 0.007785467125 Reorder the terms: 0.007785467125 + -0.1764705882x + x2 = 0.8823529412 + 0.007785467125 Combine like terms: 0.8823529412 + 0.007785467125 = 0.890138408325 0.007785467125 + -0.1764705882x + x2 = 0.890138408325 Factor a perfect square on the left side: (x + -0.0882352941)(x + -0.0882352941) = 0.890138408325 Calculate the square root of the right side: 0.943471467 Break this problem into two subproblems by setting (x + -0.0882352941) equal to 0.943471467 and -0.943471467.Subproblem 1
x + -0.0882352941 = 0.943471467 Simplifying x + -0.0882352941 = 0.943471467 Reorder the terms: -0.0882352941 + x = 0.943471467 Solving -0.0882352941 + x = 0.943471467 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 = 0.943471467 + 0.0882352941 Combine like terms: -0.0882352941 + 0.0882352941 = 0.0000000000 0.0000000000 + x = 0.943471467 + 0.0882352941 x = 0.943471467 + 0.0882352941 Combine like terms: 0.943471467 + 0.0882352941 = 1.0317067611 x = 1.0317067611 Simplifying x = 1.0317067611Subproblem 2
x + -0.0882352941 = -0.943471467 Simplifying x + -0.0882352941 = -0.943471467 Reorder the terms: -0.0882352941 + x = -0.943471467 Solving -0.0882352941 + x = -0.943471467 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 = -0.943471467 + 0.0882352941 Combine like terms: -0.0882352941 + 0.0882352941 = 0.0000000000 0.0000000000 + x = -0.943471467 + 0.0882352941 x = -0.943471467 + 0.0882352941 Combine like terms: -0.943471467 + 0.0882352941 = -0.8552361729 x = -0.8552361729 Simplifying x = -0.8552361729Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0317067611, -0.8552361729}
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