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Simplifying 17x2 + -6x = 9 Reorder the terms: -6x + 17x2 = 9 Solving -6x + 17x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -6x + 17x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -6x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.5294117647 + -0.3529411765x + x2 = 0 Move the constant term to the right: Add '0.5294117647' to each side of the equation. -0.5294117647 + -0.3529411765x + 0.5294117647 + x2 = 0 + 0.5294117647 Reorder the terms: -0.5294117647 + 0.5294117647 + -0.3529411765x + x2 = 0 + 0.5294117647 Combine like terms: -0.5294117647 + 0.5294117647 = 0.0000000000 0.0000000000 + -0.3529411765x + x2 = 0 + 0.5294117647 -0.3529411765x + x2 = 0 + 0.5294117647 Combine like terms: 0 + 0.5294117647 = 0.5294117647 -0.3529411765x + x2 = 0.5294117647 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 = 0.5294117647 + 0.03114186853 Reorder the terms: 0.03114186853 + -0.3529411765x + x2 = 0.5294117647 + 0.03114186853 Combine like terms: 0.5294117647 + 0.03114186853 = 0.56055363323 0.03114186853 + -0.3529411765x + x2 = 0.56055363323 Factor a perfect square on the left side: (x + -0.1764705883)(x + -0.1764705883) = 0.56055363323 Calculate the square root of the right side: 0.748701298 Break this problem into two subproblems by setting (x + -0.1764705883) equal to 0.748701298 and -0.748701298.Subproblem 1
x + -0.1764705883 = 0.748701298 Simplifying x + -0.1764705883 = 0.748701298 Reorder the terms: -0.1764705883 + x = 0.748701298 Solving -0.1764705883 + x = 0.748701298 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 = 0.748701298 + 0.1764705883 Combine like terms: -0.1764705883 + 0.1764705883 = 0.0000000000 0.0000000000 + x = 0.748701298 + 0.1764705883 x = 0.748701298 + 0.1764705883 Combine like terms: 0.748701298 + 0.1764705883 = 0.9251718863 x = 0.9251718863 Simplifying x = 0.9251718863Subproblem 2
x + -0.1764705883 = -0.748701298 Simplifying x + -0.1764705883 = -0.748701298 Reorder the terms: -0.1764705883 + x = -0.748701298 Solving -0.1764705883 + x = -0.748701298 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 = -0.748701298 + 0.1764705883 Combine like terms: -0.1764705883 + 0.1764705883 = 0.0000000000 0.0000000000 + x = -0.748701298 + 0.1764705883 x = -0.748701298 + 0.1764705883 Combine like terms: -0.748701298 + 0.1764705883 = -0.5722307097 x = -0.5722307097 Simplifying x = -0.5722307097Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9251718863, -0.5722307097}
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