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Simplifying 16x2 + 220x + -41 = 0 Reorder the terms: -41 + 220x + 16x2 = 0 Solving -41 + 220x + 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'. -2.5625 + 13.75x + x2 = 0 Move the constant term to the right: Add '2.5625' to each side of the equation. -2.5625 + 13.75x + 2.5625 + x2 = 0 + 2.5625 Reorder the terms: -2.5625 + 2.5625 + 13.75x + x2 = 0 + 2.5625 Combine like terms: -2.5625 + 2.5625 = 0.0000 0.0000 + 13.75x + x2 = 0 + 2.5625 13.75x + x2 = 0 + 2.5625 Combine like terms: 0 + 2.5625 = 2.5625 13.75x + x2 = 2.5625 The x term is 13.75x. Take half its coefficient (6.875). Square it (47.265625) and add it to both sides. Add '47.265625' to each side of the equation. 13.75x + 47.265625 + x2 = 2.5625 + 47.265625 Reorder the terms: 47.265625 + 13.75x + x2 = 2.5625 + 47.265625 Combine like terms: 2.5625 + 47.265625 = 49.828125 47.265625 + 13.75x + x2 = 49.828125 Factor a perfect square on the left side: (x + 6.875)(x + 6.875) = 49.828125 Calculate the square root of the right side: 7.058903952 Break this problem into two subproblems by setting (x + 6.875) equal to 7.058903952 and -7.058903952.Subproblem 1
x + 6.875 = 7.058903952 Simplifying x + 6.875 = 7.058903952 Reorder the terms: 6.875 + x = 7.058903952 Solving 6.875 + x = 7.058903952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.875' to each side of the equation. 6.875 + -6.875 + x = 7.058903952 + -6.875 Combine like terms: 6.875 + -6.875 = 0.000 0.000 + x = 7.058903952 + -6.875 x = 7.058903952 + -6.875 Combine like terms: 7.058903952 + -6.875 = 0.183903952 x = 0.183903952 Simplifying x = 0.183903952Subproblem 2
x + 6.875 = -7.058903952 Simplifying x + 6.875 = -7.058903952 Reorder the terms: 6.875 + x = -7.058903952 Solving 6.875 + x = -7.058903952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.875' to each side of the equation. 6.875 + -6.875 + x = -7.058903952 + -6.875 Combine like terms: 6.875 + -6.875 = 0.000 0.000 + x = -7.058903952 + -6.875 x = -7.058903952 + -6.875 Combine like terms: -7.058903952 + -6.875 = -13.933903952 x = -13.933903952 Simplifying x = -13.933903952Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.183903952, -13.933903952}
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