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Simplifying 0 = -9x2 + 259x + 1800 Reorder the terms: 0 = 1800 + 259x + -9x2 Solving 0 = 1800 + 259x + -9x2 Solving for variable 'x'. Combine like terms: 0 + -1800 = -1800 -1800 + -259x + 9x2 = 1800 + 259x + -9x2 + -1800 + -259x + 9x2 Reorder the terms: -1800 + -259x + 9x2 = 1800 + -1800 + 259x + -259x + -9x2 + 9x2 Combine like terms: 1800 + -1800 = 0 -1800 + -259x + 9x2 = 0 + 259x + -259x + -9x2 + 9x2 -1800 + -259x + 9x2 = 259x + -259x + -9x2 + 9x2 Combine like terms: 259x + -259x = 0 -1800 + -259x + 9x2 = 0 + -9x2 + 9x2 -1800 + -259x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -1800 + -259x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -200 + -28.77777778x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -28.77777778x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -28.77777778x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -28.77777778x + x2 = 0 + 200 -28.77777778x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -28.77777778x + x2 = 200 The x term is -28.77777778x. Take half its coefficient (-14.38888889). Square it (207.0401235) and add it to both sides. Add '207.0401235' to each side of the equation. -28.77777778x + 207.0401235 + x2 = 200 + 207.0401235 Reorder the terms: 207.0401235 + -28.77777778x + x2 = 200 + 207.0401235 Combine like terms: 200 + 207.0401235 = 407.0401235 207.0401235 + -28.77777778x + x2 = 407.0401235 Factor a perfect square on the left side: (x + -14.38888889)(x + -14.38888889) = 407.0401235 Calculate the square root of the right side: 20.175235401 Break this problem into two subproblems by setting (x + -14.38888889) equal to 20.175235401 and -20.175235401.Subproblem 1
x + -14.38888889 = 20.175235401 Simplifying x + -14.38888889 = 20.175235401 Reorder the terms: -14.38888889 + x = 20.175235401 Solving -14.38888889 + x = 20.175235401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.38888889' to each side of the equation. -14.38888889 + 14.38888889 + x = 20.175235401 + 14.38888889 Combine like terms: -14.38888889 + 14.38888889 = 0.00000000 0.00000000 + x = 20.175235401 + 14.38888889 x = 20.175235401 + 14.38888889 Combine like terms: 20.175235401 + 14.38888889 = 34.564124291 x = 34.564124291 Simplifying x = 34.564124291Subproblem 2
x + -14.38888889 = -20.175235401 Simplifying x + -14.38888889 = -20.175235401 Reorder the terms: -14.38888889 + x = -20.175235401 Solving -14.38888889 + x = -20.175235401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.38888889' to each side of the equation. -14.38888889 + 14.38888889 + x = -20.175235401 + 14.38888889 Combine like terms: -14.38888889 + 14.38888889 = 0.00000000 0.00000000 + x = -20.175235401 + 14.38888889 x = -20.175235401 + 14.38888889 Combine like terms: -20.175235401 + 14.38888889 = -5.786346511 x = -5.786346511 Simplifying x = -5.786346511Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.564124291, -5.786346511}
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