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Simplifying x = -16x2 + 96x + 3 Reorder the terms: x = 3 + 96x + -16x2 Solving x = 3 + 96x + -16x2 Solving for variable 'x'. Reorder the terms: -3 + x + -96x + 16x2 = 3 + 96x + -16x2 + -3 + -96x + 16x2 Combine like terms: x + -96x = -95x -3 + -95x + 16x2 = 3 + 96x + -16x2 + -3 + -96x + 16x2 Reorder the terms: -3 + -95x + 16x2 = 3 + -3 + 96x + -96x + -16x2 + 16x2 Combine like terms: 3 + -3 = 0 -3 + -95x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2 -3 + -95x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 -3 + -95x + 16x2 = 0 + -16x2 + 16x2 -3 + -95x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -3 + -95x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -5.9375x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -5.9375x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -5.9375x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -5.9375x + x2 = 0 + 0.1875 -5.9375x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -5.9375x + x2 = 0.1875 The x term is -5.9375x. Take half its coefficient (-2.96875). Square it (8.813476563) and add it to both sides. Add '8.813476563' to each side of the equation. -5.9375x + 8.813476563 + x2 = 0.1875 + 8.813476563 Reorder the terms: 8.813476563 + -5.9375x + x2 = 0.1875 + 8.813476563 Combine like terms: 0.1875 + 8.813476563 = 9.000976563 8.813476563 + -5.9375x + x2 = 9.000976563 Factor a perfect square on the left side: (x + -2.96875)(x + -2.96875) = 9.000976563 Calculate the square root of the right side: 3.000162756 Break this problem into two subproblems by setting (x + -2.96875) equal to 3.000162756 and -3.000162756.Subproblem 1
x + -2.96875 = 3.000162756 Simplifying x + -2.96875 = 3.000162756 Reorder the terms: -2.96875 + x = 3.000162756 Solving -2.96875 + x = 3.000162756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + x = 3.000162756 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + x = 3.000162756 + 2.96875 x = 3.000162756 + 2.96875 Combine like terms: 3.000162756 + 2.96875 = 5.968912756 x = 5.968912756 Simplifying x = 5.968912756Subproblem 2
x + -2.96875 = -3.000162756 Simplifying x + -2.96875 = -3.000162756 Reorder the terms: -2.96875 + x = -3.000162756 Solving -2.96875 + x = -3.000162756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + x = -3.000162756 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + x = -3.000162756 + 2.96875 x = -3.000162756 + 2.96875 Combine like terms: -3.000162756 + 2.96875 = -0.031412756 x = -0.031412756 Simplifying x = -0.031412756Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.968912756, -0.031412756}
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