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Simplifying 182.68 = 92x + -9.81x2 Solving 182.68 = 92x + -9.81x2 Solving for variable 'x'. Reorder the terms: 182.68 + -92x + 9.81x2 = 92x + -92x + -9.81x2 + 9.81x2 Combine like terms: 92x + -92x = 0 182.68 + -92x + 9.81x2 = 0 + -9.81x2 + 9.81x2 182.68 + -92x + 9.81x2 = -9.81x2 + 9.81x2 Combine like terms: -9.81x2 + 9.81x2 = 0.00 182.68 + -92x + 9.81x2 = 0.00 Begin completing the square. Divide all terms by 9.81 the coefficient of the squared term: Divide each side by '9.81'. 18.62181448 + -9.378185525x + x2 = 0 Move the constant term to the right: Add '-18.62181448' to each side of the equation. 18.62181448 + -9.378185525x + -18.62181448 + x2 = 0 + -18.62181448 Reorder the terms: 18.62181448 + -18.62181448 + -9.378185525x + x2 = 0 + -18.62181448 Combine like terms: 18.62181448 + -18.62181448 = 0.00000000 0.00000000 + -9.378185525x + x2 = 0 + -18.62181448 -9.378185525x + x2 = 0 + -18.62181448 Combine like terms: 0 + -18.62181448 = -18.62181448 -9.378185525x + x2 = -18.62181448 The x term is -9.378185525x. Take half its coefficient (-4.689092763). Square it (21.98759094) and add it to both sides. Add '21.98759094' to each side of the equation. -9.378185525x + 21.98759094 + x2 = -18.62181448 + 21.98759094 Reorder the terms: 21.98759094 + -9.378185525x + x2 = -18.62181448 + 21.98759094 Combine like terms: -18.62181448 + 21.98759094 = 3.36577646 21.98759094 + -9.378185525x + x2 = 3.36577646 Factor a perfect square on the left side: (x + -4.689092763)(x + -4.689092763) = 3.36577646 Calculate the square root of the right side: 1.83460526 Break this problem into two subproblems by setting (x + -4.689092763) equal to 1.83460526 and -1.83460526.Subproblem 1
x + -4.689092763 = 1.83460526 Simplifying x + -4.689092763 = 1.83460526 Reorder the terms: -4.689092763 + x = 1.83460526 Solving -4.689092763 + x = 1.83460526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.689092763' to each side of the equation. -4.689092763 + 4.689092763 + x = 1.83460526 + 4.689092763 Combine like terms: -4.689092763 + 4.689092763 = 0.000000000 0.000000000 + x = 1.83460526 + 4.689092763 x = 1.83460526 + 4.689092763 Combine like terms: 1.83460526 + 4.689092763 = 6.523698023 x = 6.523698023 Simplifying x = 6.523698023Subproblem 2
x + -4.689092763 = -1.83460526 Simplifying x + -4.689092763 = -1.83460526 Reorder the terms: -4.689092763 + x = -1.83460526 Solving -4.689092763 + x = -1.83460526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.689092763' to each side of the equation. -4.689092763 + 4.689092763 + x = -1.83460526 + 4.689092763 Combine like terms: -4.689092763 + 4.689092763 = 0.000000000 0.000000000 + x = -1.83460526 + 4.689092763 x = -1.83460526 + 4.689092763 Combine like terms: -1.83460526 + 4.689092763 = 2.854487503 x = 2.854487503 Simplifying x = 2.854487503Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.523698023, 2.854487503}
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