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Simplifying 9x2 + -25x + -116 = 0 Reorder the terms: -116 + -25x + 9x2 = 0 Solving -116 + -25x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -12.88888889 + -2.777777778x + x2 = 0 Move the constant term to the right: Add '12.88888889' to each side of the equation. -12.88888889 + -2.777777778x + 12.88888889 + x2 = 0 + 12.88888889 Reorder the terms: -12.88888889 + 12.88888889 + -2.777777778x + x2 = 0 + 12.88888889 Combine like terms: -12.88888889 + 12.88888889 = 0.00000000 0.00000000 + -2.777777778x + x2 = 0 + 12.88888889 -2.777777778x + x2 = 0 + 12.88888889 Combine like terms: 0 + 12.88888889 = 12.88888889 -2.777777778x + x2 = 12.88888889 The x term is -2.777777778x. Take half its coefficient (-1.388888889). Square it (1.929012346) and add it to both sides. Add '1.929012346' to each side of the equation. -2.777777778x + 1.929012346 + x2 = 12.88888889 + 1.929012346 Reorder the terms: 1.929012346 + -2.777777778x + x2 = 12.88888889 + 1.929012346 Combine like terms: 12.88888889 + 1.929012346 = 14.817901236 1.929012346 + -2.777777778x + x2 = 14.817901236 Factor a perfect square on the left side: (x + -1.388888889)(x + -1.388888889) = 14.817901236 Calculate the square root of the right side: 3.849402712 Break this problem into two subproblems by setting (x + -1.388888889) equal to 3.849402712 and -3.849402712.Subproblem 1
x + -1.388888889 = 3.849402712 Simplifying x + -1.388888889 = 3.849402712 Reorder the terms: -1.388888889 + x = 3.849402712 Solving -1.388888889 + x = 3.849402712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x = 3.849402712 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = 3.849402712 + 1.388888889 x = 3.849402712 + 1.388888889 Combine like terms: 3.849402712 + 1.388888889 = 5.238291601 x = 5.238291601 Simplifying x = 5.238291601Subproblem 2
x + -1.388888889 = -3.849402712 Simplifying x + -1.388888889 = -3.849402712 Reorder the terms: -1.388888889 + x = -3.849402712 Solving -1.388888889 + x = -3.849402712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x = -3.849402712 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = -3.849402712 + 1.388888889 x = -3.849402712 + 1.388888889 Combine like terms: -3.849402712 + 1.388888889 = -2.460513823 x = -2.460513823 Simplifying x = -2.460513823Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.238291601, -2.460513823}
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