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Simplifying 0 = 400x + -11x2 + 2 Reorder the terms: 0 = 2 + 400x + -11x2 Solving 0 = 2 + 400x + -11x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -400x + 11x2 = 2 + 400x + -11x2 + -2 + -400x + 11x2 Reorder the terms: -2 + -400x + 11x2 = 2 + -2 + 400x + -400x + -11x2 + 11x2 Combine like terms: 2 + -2 = 0 -2 + -400x + 11x2 = 0 + 400x + -400x + -11x2 + 11x2 -2 + -400x + 11x2 = 400x + -400x + -11x2 + 11x2 Combine like terms: 400x + -400x = 0 -2 + -400x + 11x2 = 0 + -11x2 + 11x2 -2 + -400x + 11x2 = -11x2 + 11x2 Combine like terms: -11x2 + 11x2 = 0 -2 + -400x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.1818181818 + -36.36363636x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + -36.36363636x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + -36.36363636x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + -36.36363636x + x2 = 0 + 0.1818181818 -36.36363636x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 -36.36363636x + x2 = 0.1818181818 The x term is -36.36363636x. Take half its coefficient (-18.18181818). Square it (330.5785123) and add it to both sides. Add '330.5785123' to each side of the equation. -36.36363636x + 330.5785123 + x2 = 0.1818181818 + 330.5785123 Reorder the terms: 330.5785123 + -36.36363636x + x2 = 0.1818181818 + 330.5785123 Combine like terms: 0.1818181818 + 330.5785123 = 330.7603304818 330.5785123 + -36.36363636x + x2 = 330.7603304818 Factor a perfect square on the left side: (x + -18.18181818)(x + -18.18181818) = 330.7603304818 Calculate the square root of the right side: 18.186817492 Break this problem into two subproblems by setting (x + -18.18181818) equal to 18.186817492 and -18.186817492.Subproblem 1
x + -18.18181818 = 18.186817492 Simplifying x + -18.18181818 = 18.186817492 Reorder the terms: -18.18181818 + x = 18.186817492 Solving -18.18181818 + x = 18.186817492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.18181818' to each side of the equation. -18.18181818 + 18.18181818 + x = 18.186817492 + 18.18181818 Combine like terms: -18.18181818 + 18.18181818 = 0.00000000 0.00000000 + x = 18.186817492 + 18.18181818 x = 18.186817492 + 18.18181818 Combine like terms: 18.186817492 + 18.18181818 = 36.368635672 x = 36.368635672 Simplifying x = 36.368635672Subproblem 2
x + -18.18181818 = -18.186817492 Simplifying x + -18.18181818 = -18.186817492 Reorder the terms: -18.18181818 + x = -18.186817492 Solving -18.18181818 + x = -18.186817492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.18181818' to each side of the equation. -18.18181818 + 18.18181818 + x = -18.186817492 + 18.18181818 Combine like terms: -18.18181818 + 18.18181818 = 0.00000000 0.00000000 + x = -18.186817492 + 18.18181818 x = -18.186817492 + 18.18181818 Combine like terms: -18.186817492 + 18.18181818 = -0.004999312 x = -0.004999312 Simplifying x = -0.004999312Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.368635672, -0.004999312}
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