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Simplifying 0 = -16x2 + 50x + 500 Reorder the terms: 0 = 500 + 50x + -16x2 Solving 0 = 500 + 50x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -500 = -500 -500 + -50x + 16x2 = 500 + 50x + -16x2 + -500 + -50x + 16x2 Reorder the terms: -500 + -50x + 16x2 = 500 + -500 + 50x + -50x + -16x2 + 16x2 Combine like terms: 500 + -500 = 0 -500 + -50x + 16x2 = 0 + 50x + -50x + -16x2 + 16x2 -500 + -50x + 16x2 = 50x + -50x + -16x2 + 16x2 Combine like terms: 50x + -50x = 0 -500 + -50x + 16x2 = 0 + -16x2 + 16x2 -500 + -50x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -500 + -50x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-250 + -25x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-250 + -25x + 8x2)' equal to zero and attempt to solve: Simplifying -250 + -25x + 8x2 = 0 Solving -250 + -25x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -31.25 + -3.125x + x2 = 0 Move the constant term to the right: Add '31.25' to each side of the equation. -31.25 + -3.125x + 31.25 + x2 = 0 + 31.25 Reorder the terms: -31.25 + 31.25 + -3.125x + x2 = 0 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + -3.125x + x2 = 0 + 31.25 -3.125x + x2 = 0 + 31.25 Combine like terms: 0 + 31.25 = 31.25 -3.125x + x2 = 31.25 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 = 31.25 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 31.25 + 2.44140625 Combine like terms: 31.25 + 2.44140625 = 33.69140625 2.44140625 + -3.125x + x2 = 33.69140625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 33.69140625 Calculate the square root of the right side: 5.804429882 Break this problem into two subproblems by setting (x + -1.5625) equal to 5.804429882 and -5.804429882.Subproblem 1
x + -1.5625 = 5.804429882 Simplifying x + -1.5625 = 5.804429882 Reorder the terms: -1.5625 + x = 5.804429882 Solving -1.5625 + x = 5.804429882 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 = 5.804429882 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 5.804429882 + 1.5625 x = 5.804429882 + 1.5625 Combine like terms: 5.804429882 + 1.5625 = 7.366929882 x = 7.366929882 Simplifying x = 7.366929882Subproblem 2
x + -1.5625 = -5.804429882 Simplifying x + -1.5625 = -5.804429882 Reorder the terms: -1.5625 + x = -5.804429882 Solving -1.5625 + x = -5.804429882 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 = -5.804429882 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -5.804429882 + 1.5625 x = -5.804429882 + 1.5625 Combine like terms: -5.804429882 + 1.5625 = -4.241929882 x = -4.241929882 Simplifying x = -4.241929882Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.366929882, -4.241929882}Solution
x = {7.366929882, -4.241929882}
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