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Simplifying -16.1x2 + 2499x + 5.9 = 0 Reorder the terms: 5.9 + 2499x + -16.1x2 = 0 Solving 5.9 + 2499x + -16.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16.1 the coefficient of the squared term: Divide each side by '-16.1'. -0.3664596273 + -155.2173913x + x2 = 0 Move the constant term to the right: Add '0.3664596273' to each side of the equation. -0.3664596273 + -155.2173913x + 0.3664596273 + x2 = 0 + 0.3664596273 Reorder the terms: -0.3664596273 + 0.3664596273 + -155.2173913x + x2 = 0 + 0.3664596273 Combine like terms: -0.3664596273 + 0.3664596273 = 0.0000000000 0.0000000000 + -155.2173913x + x2 = 0 + 0.3664596273 -155.2173913x + x2 = 0 + 0.3664596273 Combine like terms: 0 + 0.3664596273 = 0.3664596273 -155.2173913x + x2 = 0.3664596273 The x term is -155.2173913x. Take half its coefficient (-77.60869565). Square it (6023.109640) and add it to both sides. Add '6023.109640' to each side of the equation. -155.2173913x + 6023.109640 + x2 = 0.3664596273 + 6023.109640 Reorder the terms: 6023.109640 + -155.2173913x + x2 = 0.3664596273 + 6023.109640 Combine like terms: 0.3664596273 + 6023.109640 = 6023.4760996273 6023.109640 + -155.2173913x + x2 = 6023.4760996273 Factor a perfect square on the left side: (x + -77.60869565)(x + -77.60869565) = 6023.4760996273 Calculate the square root of the right side: 77.611056555 Break this problem into two subproblems by setting (x + -77.60869565) equal to 77.611056555 and -77.611056555.Subproblem 1
x + -77.60869565 = 77.611056555 Simplifying x + -77.60869565 = 77.611056555 Reorder the terms: -77.60869565 + x = 77.611056555 Solving -77.60869565 + x = 77.611056555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '77.60869565' to each side of the equation. -77.60869565 + 77.60869565 + x = 77.611056555 + 77.60869565 Combine like terms: -77.60869565 + 77.60869565 = 0.00000000 0.00000000 + x = 77.611056555 + 77.60869565 x = 77.611056555 + 77.60869565 Combine like terms: 77.611056555 + 77.60869565 = 155.219752205 x = 155.219752205 Simplifying x = 155.219752205Subproblem 2
x + -77.60869565 = -77.611056555 Simplifying x + -77.60869565 = -77.611056555 Reorder the terms: -77.60869565 + x = -77.611056555 Solving -77.60869565 + x = -77.611056555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '77.60869565' to each side of the equation. -77.60869565 + 77.60869565 + x = -77.611056555 + 77.60869565 Combine like terms: -77.60869565 + 77.60869565 = 0.00000000 0.00000000 + x = -77.611056555 + 77.60869565 x = -77.611056555 + 77.60869565 Combine like terms: -77.611056555 + 77.60869565 = -0.002360905 x = -0.002360905 Simplifying x = -0.002360905Solution
The solution to the problem is based on the solutions from the subproblems. x = {155.219752205, -0.002360905}
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