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Simplifying 17x2 + 128x + 216 = 0 Reorder the terms: 216 + 128x + 17x2 = 0 Solving 216 + 128x + 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'. 12.70588235 + 7.529411765x + x2 = 0 Move the constant term to the right: Add '-12.70588235' to each side of the equation. 12.70588235 + 7.529411765x + -12.70588235 + x2 = 0 + -12.70588235 Reorder the terms: 12.70588235 + -12.70588235 + 7.529411765x + x2 = 0 + -12.70588235 Combine like terms: 12.70588235 + -12.70588235 = 0.00000000 0.00000000 + 7.529411765x + x2 = 0 + -12.70588235 7.529411765x + x2 = 0 + -12.70588235 Combine like terms: 0 + -12.70588235 = -12.70588235 7.529411765x + x2 = -12.70588235 The x term is 7.529411765x. Take half its coefficient (3.764705883). Square it (14.17301039) and add it to both sides. Add '14.17301039' to each side of the equation. 7.529411765x + 14.17301039 + x2 = -12.70588235 + 14.17301039 Reorder the terms: 14.17301039 + 7.529411765x + x2 = -12.70588235 + 14.17301039 Combine like terms: -12.70588235 + 14.17301039 = 1.46712804 14.17301039 + 7.529411765x + x2 = 1.46712804 Factor a perfect square on the left side: (x + 3.764705883)(x + 3.764705883) = 1.46712804 Calculate the square root of the right side: 1.21125061 Break this problem into two subproblems by setting (x + 3.764705883) equal to 1.21125061 and -1.21125061.Subproblem 1
x + 3.764705883 = 1.21125061 Simplifying x + 3.764705883 = 1.21125061 Reorder the terms: 3.764705883 + x = 1.21125061 Solving 3.764705883 + x = 1.21125061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.764705883' to each side of the equation. 3.764705883 + -3.764705883 + x = 1.21125061 + -3.764705883 Combine like terms: 3.764705883 + -3.764705883 = 0.000000000 0.000000000 + x = 1.21125061 + -3.764705883 x = 1.21125061 + -3.764705883 Combine like terms: 1.21125061 + -3.764705883 = -2.553455273 x = -2.553455273 Simplifying x = -2.553455273Subproblem 2
x + 3.764705883 = -1.21125061 Simplifying x + 3.764705883 = -1.21125061 Reorder the terms: 3.764705883 + x = -1.21125061 Solving 3.764705883 + x = -1.21125061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.764705883' to each side of the equation. 3.764705883 + -3.764705883 + x = -1.21125061 + -3.764705883 Combine like terms: 3.764705883 + -3.764705883 = 0.000000000 0.000000000 + x = -1.21125061 + -3.764705883 x = -1.21125061 + -3.764705883 Combine like terms: -1.21125061 + -3.764705883 = -4.975956493 x = -4.975956493 Simplifying x = -4.975956493Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.553455273, -4.975956493}
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