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Simplifying 9x2 + -25x + -94 = 0 Reorder the terms: -94 + -25x + 9x2 = 0 Solving -94 + -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'. -10.44444444 + -2.777777778x + x2 = 0 Move the constant term to the right: Add '10.44444444' to each side of the equation. -10.44444444 + -2.777777778x + 10.44444444 + x2 = 0 + 10.44444444 Reorder the terms: -10.44444444 + 10.44444444 + -2.777777778x + x2 = 0 + 10.44444444 Combine like terms: -10.44444444 + 10.44444444 = 0.00000000 0.00000000 + -2.777777778x + x2 = 0 + 10.44444444 -2.777777778x + x2 = 0 + 10.44444444 Combine like terms: 0 + 10.44444444 = 10.44444444 -2.777777778x + x2 = 10.44444444 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 = 10.44444444 + 1.929012346 Reorder the terms: 1.929012346 + -2.777777778x + x2 = 10.44444444 + 1.929012346 Combine like terms: 10.44444444 + 1.929012346 = 12.373456786 1.929012346 + -2.777777778x + x2 = 12.373456786 Factor a perfect square on the left side: (x + -1.388888889)(x + -1.388888889) = 12.373456786 Calculate the square root of the right side: 3.51759247 Break this problem into two subproblems by setting (x + -1.388888889) equal to 3.51759247 and -3.51759247.Subproblem 1
x + -1.388888889 = 3.51759247 Simplifying x + -1.388888889 = 3.51759247 Reorder the terms: -1.388888889 + x = 3.51759247 Solving -1.388888889 + x = 3.51759247 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 = 3.51759247 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = 3.51759247 + 1.388888889 x = 3.51759247 + 1.388888889 Combine like terms: 3.51759247 + 1.388888889 = 4.906481359 x = 4.906481359 Simplifying x = 4.906481359Subproblem 2
x + -1.388888889 = -3.51759247 Simplifying x + -1.388888889 = -3.51759247 Reorder the terms: -1.388888889 + x = -3.51759247 Solving -1.388888889 + x = -3.51759247 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 = -3.51759247 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = -3.51759247 + 1.388888889 x = -3.51759247 + 1.388888889 Combine like terms: -3.51759247 + 1.388888889 = -2.128703581 x = -2.128703581 Simplifying x = -2.128703581Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.906481359, -2.128703581}
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