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Simplifying 0 = -2.625x2 + 24.1x + -9.95 Reorder the terms: 0 = -9.95 + 24.1x + -2.625x2 Solving 0 = -9.95 + 24.1x + -2.625x2 Solving for variable 'x'. Combine like terms: 0 + 9.95 = 9.95 9.95 + -24.1x + 2.625x2 = -9.95 + 24.1x + -2.625x2 + 9.95 + -24.1x + 2.625x2 Reorder the terms: 9.95 + -24.1x + 2.625x2 = -9.95 + 9.95 + 24.1x + -24.1x + -2.625x2 + 2.625x2 Combine like terms: -9.95 + 9.95 = 0.00 9.95 + -24.1x + 2.625x2 = 0.00 + 24.1x + -24.1x + -2.625x2 + 2.625x2 9.95 + -24.1x + 2.625x2 = 24.1x + -24.1x + -2.625x2 + 2.625x2 Combine like terms: 24.1x + -24.1x = 0.0 9.95 + -24.1x + 2.625x2 = 0.0 + -2.625x2 + 2.625x2 9.95 + -24.1x + 2.625x2 = -2.625x2 + 2.625x2 Combine like terms: -2.625x2 + 2.625x2 = 0.000 9.95 + -24.1x + 2.625x2 = 0.000 Begin completing the square. Divide all terms by 2.625 the coefficient of the squared term: Divide each side by '2.625'. 3.79047619 + -9.180952381x + x2 = 0 Move the constant term to the right: Add '-3.79047619' to each side of the equation. 3.79047619 + -9.180952381x + -3.79047619 + x2 = 0 + -3.79047619 Reorder the terms: 3.79047619 + -3.79047619 + -9.180952381x + x2 = 0 + -3.79047619 Combine like terms: 3.79047619 + -3.79047619 = 0.00000000 0.00000000 + -9.180952381x + x2 = 0 + -3.79047619 -9.180952381x + x2 = 0 + -3.79047619 Combine like terms: 0 + -3.79047619 = -3.79047619 -9.180952381x + x2 = -3.79047619 The x term is -9.180952381x. Take half its coefficient (-4.590476191). Square it (21.07247166) and add it to both sides. Add '21.07247166' to each side of the equation. -9.180952381x + 21.07247166 + x2 = -3.79047619 + 21.07247166 Reorder the terms: 21.07247166 + -9.180952381x + x2 = -3.79047619 + 21.07247166 Combine like terms: -3.79047619 + 21.07247166 = 17.28199547 21.07247166 + -9.180952381x + x2 = 17.28199547 Factor a perfect square on the left side: (x + -4.590476191)(x + -4.590476191) = 17.28199547 Calculate the square root of the right side: 4.157161949 Break this problem into two subproblems by setting (x + -4.590476191) equal to 4.157161949 and -4.157161949.Subproblem 1
x + -4.590476191 = 4.157161949 Simplifying x + -4.590476191 = 4.157161949 Reorder the terms: -4.590476191 + x = 4.157161949 Solving -4.590476191 + x = 4.157161949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.590476191' to each side of the equation. -4.590476191 + 4.590476191 + x = 4.157161949 + 4.590476191 Combine like terms: -4.590476191 + 4.590476191 = 0.000000000 0.000000000 + x = 4.157161949 + 4.590476191 x = 4.157161949 + 4.590476191 Combine like terms: 4.157161949 + 4.590476191 = 8.74763814 x = 8.74763814 Simplifying x = 8.74763814Subproblem 2
x + -4.590476191 = -4.157161949 Simplifying x + -4.590476191 = -4.157161949 Reorder the terms: -4.590476191 + x = -4.157161949 Solving -4.590476191 + x = -4.157161949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.590476191' to each side of the equation. -4.590476191 + 4.590476191 + x = -4.157161949 + 4.590476191 Combine like terms: -4.590476191 + 4.590476191 = 0.000000000 0.000000000 + x = -4.157161949 + 4.590476191 x = -4.157161949 + 4.590476191 Combine like terms: -4.157161949 + 4.590476191 = 0.433314242 x = 0.433314242 Simplifying x = 0.433314242Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.74763814, 0.433314242}
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