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Simplifying 0 = -16x2 + 30x + 5 Reorder the terms: 0 = 5 + 30x + -16x2 Solving 0 = 5 + 30x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -30x + 16x2 = 5 + 30x + -16x2 + -5 + -30x + 16x2 Reorder the terms: -5 + -30x + 16x2 = 5 + -5 + 30x + -30x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 -5 + -30x + 16x2 = 0 + 30x + -30x + -16x2 + 16x2 -5 + -30x + 16x2 = 30x + -30x + -16x2 + 16x2 Combine like terms: 30x + -30x = 0 -5 + -30x + 16x2 = 0 + -16x2 + 16x2 -5 + -30x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -5 + -30x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -1.875x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -1.875x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -1.875x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -1.875x + x2 = 0 + 0.3125 -1.875x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -1.875x + x2 = 0.3125 The x term is -1.875x. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875x + 0.87890625 + x2 = 0.3125 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = 0.3125 + 0.87890625 Combine like terms: 0.3125 + 0.87890625 = 1.19140625 0.87890625 + -1.875x + x2 = 1.19140625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 1.19140625 Calculate the square root of the right side: 1.091515575 Break this problem into two subproblems by setting (x + -0.9375) equal to 1.091515575 and -1.091515575.Subproblem 1
x + -0.9375 = 1.091515575 Simplifying x + -0.9375 = 1.091515575 Reorder the terms: -0.9375 + x = 1.091515575 Solving -0.9375 + x = 1.091515575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = 1.091515575 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 1.091515575 + 0.9375 x = 1.091515575 + 0.9375 Combine like terms: 1.091515575 + 0.9375 = 2.029015575 x = 2.029015575 Simplifying x = 2.029015575Subproblem 2
x + -0.9375 = -1.091515575 Simplifying x + -0.9375 = -1.091515575 Reorder the terms: -0.9375 + x = -1.091515575 Solving -0.9375 + x = -1.091515575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = -1.091515575 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -1.091515575 + 0.9375 x = -1.091515575 + 0.9375 Combine like terms: -1.091515575 + 0.9375 = -0.154015575 x = -0.154015575 Simplifying x = -0.154015575Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.029015575, -0.154015575}
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