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Simplifying 0 = -16x2 + 50x + 15 Reorder the terms: 0 = 15 + 50x + -16x2 Solving 0 = 15 + 50x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + -50x + 16x2 = 15 + 50x + -16x2 + -15 + -50x + 16x2 Reorder the terms: -15 + -50x + 16x2 = 15 + -15 + 50x + -50x + -16x2 + 16x2 Combine like terms: 15 + -15 = 0 -15 + -50x + 16x2 = 0 + 50x + -50x + -16x2 + 16x2 -15 + -50x + 16x2 = 50x + -50x + -16x2 + 16x2 Combine like terms: 50x + -50x = 0 -15 + -50x + 16x2 = 0 + -16x2 + 16x2 -15 + -50x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -15 + -50x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + -3.125x + x2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -3.125x + 0.9375 + x2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -3.125x + x2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -3.125x + x2 = 0 + 0.9375 -3.125x + x2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -3.125x + x2 = 0.9375 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = 0.9375 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 0.9375 + 2.44140625 Combine like terms: 0.9375 + 2.44140625 = 3.37890625 2.44140625 + -3.125x + x2 = 3.37890625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 3.37890625 Calculate the square root of the right side: 1.838180146 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.838180146 and -1.838180146.Subproblem 1
x + -1.5625 = 1.838180146 Simplifying x + -1.5625 = 1.838180146 Reorder the terms: -1.5625 + x = 1.838180146 Solving -1.5625 + x = 1.838180146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.838180146 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.838180146 + 1.5625 x = 1.838180146 + 1.5625 Combine like terms: 1.838180146 + 1.5625 = 3.400680146 x = 3.400680146 Simplifying x = 3.400680146Subproblem 2
x + -1.5625 = -1.838180146 Simplifying x + -1.5625 = -1.838180146 Reorder the terms: -1.5625 + x = -1.838180146 Solving -1.5625 + x = -1.838180146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.838180146 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.838180146 + 1.5625 x = -1.838180146 + 1.5625 Combine like terms: -1.838180146 + 1.5625 = -0.275680146 x = -0.275680146 Simplifying x = -0.275680146Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.400680146, -0.275680146}
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