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Simplifying 0 = -16x2 + 50x + 3 Reorder the terms: 0 = 3 + 50x + -16x2 Solving 0 = 3 + 50x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -50x + 16x2 = 3 + 50x + -16x2 + -3 + -50x + 16x2 Reorder the terms: -3 + -50x + 16x2 = 3 + -3 + 50x + -50x + -16x2 + 16x2 Combine like terms: 3 + -3 = 0 -3 + -50x + 16x2 = 0 + 50x + -50x + -16x2 + 16x2 -3 + -50x + 16x2 = 50x + -50x + -16x2 + 16x2 Combine like terms: 50x + -50x = 0 -3 + -50x + 16x2 = 0 + -16x2 + 16x2 -3 + -50x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -3 + -50x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -3.125x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -3.125x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -3.125x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -3.125x + x2 = 0 + 0.1875 -3.125x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -3.125x + x2 = 0.1875 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 = 0.1875 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 0.1875 + 2.44140625 Combine like terms: 0.1875 + 2.44140625 = 2.62890625 2.44140625 + -3.125x + x2 = 2.62890625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 2.62890625 Calculate the square root of the right side: 1.621390221 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.621390221 and -1.621390221.Subproblem 1
x + -1.5625 = 1.621390221 Simplifying x + -1.5625 = 1.621390221 Reorder the terms: -1.5625 + x = 1.621390221 Solving -1.5625 + x = 1.621390221 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 = 1.621390221 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.621390221 + 1.5625 x = 1.621390221 + 1.5625 Combine like terms: 1.621390221 + 1.5625 = 3.183890221 x = 3.183890221 Simplifying x = 3.183890221Subproblem 2
x + -1.5625 = -1.621390221 Simplifying x + -1.5625 = -1.621390221 Reorder the terms: -1.5625 + x = -1.621390221 Solving -1.5625 + x = -1.621390221 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 = -1.621390221 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.621390221 + 1.5625 x = -1.621390221 + 1.5625 Combine like terms: -1.621390221 + 1.5625 = -0.058890221 x = -0.058890221 Simplifying x = -0.058890221Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.183890221, -0.058890221}
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