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Simplifying 0 = -16x2 + 1x + 35 Reorder the terms: 0 = 35 + 1x + -16x2 Solving 0 = 35 + 1x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -35 = -35 -35 + -1x + 16x2 = 35 + 1x + -16x2 + -35 + -1x + 16x2 Reorder the terms: -35 + -1x + 16x2 = 35 + -35 + 1x + -1x + -16x2 + 16x2 Combine like terms: 35 + -35 = 0 -35 + -1x + 16x2 = 0 + 1x + -1x + -16x2 + 16x2 -35 + -1x + 16x2 = 1x + -1x + -16x2 + 16x2 Combine like terms: 1x + -1x = 0 -35 + -1x + 16x2 = 0 + -16x2 + 16x2 -35 + -1x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -35 + -1x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.1875 + -0.0625x + x2 = 0 Move the constant term to the right: Add '2.1875' to each side of the equation. -2.1875 + -0.0625x + 2.1875 + x2 = 0 + 2.1875 Reorder the terms: -2.1875 + 2.1875 + -0.0625x + x2 = 0 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + -0.0625x + x2 = 0 + 2.1875 -0.0625x + x2 = 0 + 2.1875 Combine like terms: 0 + 2.1875 = 2.1875 -0.0625x + x2 = 2.1875 The x term is -0.0625x. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625x + 0.0009765625 + x2 = 2.1875 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625x + x2 = 2.1875 + 0.0009765625 Combine like terms: 2.1875 + 0.0009765625 = 2.1884765625 0.0009765625 + -0.0625x + x2 = 2.1884765625 Factor a perfect square on the left side: (x + -0.03125)(x + -0.03125) = 2.1884765625 Calculate the square root of the right side: 1.479350047 Break this problem into two subproblems by setting (x + -0.03125) equal to 1.479350047 and -1.479350047.Subproblem 1
x + -0.03125 = 1.479350047 Simplifying x + -0.03125 = 1.479350047 Reorder the terms: -0.03125 + x = 1.479350047 Solving -0.03125 + x = 1.479350047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = 1.479350047 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = 1.479350047 + 0.03125 x = 1.479350047 + 0.03125 Combine like terms: 1.479350047 + 0.03125 = 1.510600047 x = 1.510600047 Simplifying x = 1.510600047Subproblem 2
x + -0.03125 = -1.479350047 Simplifying x + -0.03125 = -1.479350047 Reorder the terms: -0.03125 + x = -1.479350047 Solving -0.03125 + x = -1.479350047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = -1.479350047 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = -1.479350047 + 0.03125 x = -1.479350047 + 0.03125 Combine like terms: -1.479350047 + 0.03125 = -1.448100047 x = -1.448100047 Simplifying x = -1.448100047Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.510600047, -1.448100047}
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