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Simplifying x = -16x2 + 64x + 960 Reorder the terms: x = 960 + 64x + -16x2 Solving x = 960 + 64x + -16x2 Solving for variable 'x'. Reorder the terms: -960 + x + -64x + 16x2 = 960 + 64x + -16x2 + -960 + -64x + 16x2 Combine like terms: x + -64x = -63x -960 + -63x + 16x2 = 960 + 64x + -16x2 + -960 + -64x + 16x2 Reorder the terms: -960 + -63x + 16x2 = 960 + -960 + 64x + -64x + -16x2 + 16x2 Combine like terms: 960 + -960 = 0 -960 + -63x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2 -960 + -63x + 16x2 = 64x + -64x + -16x2 + 16x2 Combine like terms: 64x + -64x = 0 -960 + -63x + 16x2 = 0 + -16x2 + 16x2 -960 + -63x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -960 + -63x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -60 + -3.9375x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -3.9375x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -3.9375x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -3.9375x + x2 = 0 + 60 -3.9375x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -3.9375x + x2 = 60 The x term is -3.9375x. Take half its coefficient (-1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. -3.9375x + 3.875976563 + x2 = 60 + 3.875976563 Reorder the terms: 3.875976563 + -3.9375x + x2 = 60 + 3.875976563 Combine like terms: 60 + 3.875976563 = 63.875976563 3.875976563 + -3.9375x + x2 = 63.875976563 Factor a perfect square on the left side: (x + -1.96875)(x + -1.96875) = 63.875976563 Calculate the square root of the right side: 7.992244776 Break this problem into two subproblems by setting (x + -1.96875) equal to 7.992244776 and -7.992244776.Subproblem 1
x + -1.96875 = 7.992244776 Simplifying x + -1.96875 = 7.992244776 Reorder the terms: -1.96875 + x = 7.992244776 Solving -1.96875 + x = 7.992244776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = 7.992244776 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = 7.992244776 + 1.96875 x = 7.992244776 + 1.96875 Combine like terms: 7.992244776 + 1.96875 = 9.960994776 x = 9.960994776 Simplifying x = 9.960994776Subproblem 2
x + -1.96875 = -7.992244776 Simplifying x + -1.96875 = -7.992244776 Reorder the terms: -1.96875 + x = -7.992244776 Solving -1.96875 + x = -7.992244776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = -7.992244776 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = -7.992244776 + 1.96875 x = -7.992244776 + 1.96875 Combine like terms: -7.992244776 + 1.96875 = -6.023494776 x = -6.023494776 Simplifying x = -6.023494776Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.960994776, -6.023494776}
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