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Simplifying 16x2 + -35x + -5500 = 0 Reorder the terms: -5500 + -35x + 16x2 = 0 Solving -5500 + -35x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -343.75 + -2.1875x + x2 = 0 Move the constant term to the right: Add '343.75' to each side of the equation. -343.75 + -2.1875x + 343.75 + x2 = 0 + 343.75 Reorder the terms: -343.75 + 343.75 + -2.1875x + x2 = 0 + 343.75 Combine like terms: -343.75 + 343.75 = 0.00 0.00 + -2.1875x + x2 = 0 + 343.75 -2.1875x + x2 = 0 + 343.75 Combine like terms: 0 + 343.75 = 343.75 -2.1875x + x2 = 343.75 The x term is -2.1875x. Take half its coefficient (-1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. -2.1875x + 1.196289063 + x2 = 343.75 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875x + x2 = 343.75 + 1.196289063 Combine like terms: 343.75 + 1.196289063 = 344.946289063 1.196289063 + -2.1875x + x2 = 344.946289063 Factor a perfect square on the left side: (x + -1.09375)(x + -1.09375) = 344.946289063 Calculate the square root of the right side: 18.572729715 Break this problem into two subproblems by setting (x + -1.09375) equal to 18.572729715 and -18.572729715.Subproblem 1
x + -1.09375 = 18.572729715 Simplifying x + -1.09375 = 18.572729715 Reorder the terms: -1.09375 + x = 18.572729715 Solving -1.09375 + x = 18.572729715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + x = 18.572729715 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = 18.572729715 + 1.09375 x = 18.572729715 + 1.09375 Combine like terms: 18.572729715 + 1.09375 = 19.666479715 x = 19.666479715 Simplifying x = 19.666479715Subproblem 2
x + -1.09375 = -18.572729715 Simplifying x + -1.09375 = -18.572729715 Reorder the terms: -1.09375 + x = -18.572729715 Solving -1.09375 + x = -18.572729715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + x = -18.572729715 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + x = -18.572729715 + 1.09375 x = -18.572729715 + 1.09375 Combine like terms: -18.572729715 + 1.09375 = -17.478979715 x = -17.478979715 Simplifying x = -17.478979715Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.666479715, -17.478979715}
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