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Simplifying 9x2 + -25x + -6 = 9 Reorder the terms: -6 + -25x + 9x2 = 9 Solving -6 + -25x + 9x2 = 9 Solving for variable 'x'. Reorder the terms: -6 + -9 + -25x + 9x2 = 9 + -9 Combine like terms: -6 + -9 = -15 -15 + -25x + 9x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -15 + -25x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.666666667 + -2.777777778x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -2.777777778x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -2.777777778x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -2.777777778x + x2 = 0 + 1.666666667 -2.777777778x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -2.777777778x + x2 = 1.666666667 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 = 1.666666667 + 1.929012346 Reorder the terms: 1.929012346 + -2.777777778x + x2 = 1.666666667 + 1.929012346 Combine like terms: 1.666666667 + 1.929012346 = 3.595679013 1.929012346 + -2.777777778x + x2 = 3.595679013 Factor a perfect square on the left side: (x + -1.388888889)(x + -1.388888889) = 3.595679013 Calculate the square root of the right side: 1.896227574 Break this problem into two subproblems by setting (x + -1.388888889) equal to 1.896227574 and -1.896227574.Subproblem 1
x + -1.388888889 = 1.896227574 Simplifying x + -1.388888889 = 1.896227574 Reorder the terms: -1.388888889 + x = 1.896227574 Solving -1.388888889 + x = 1.896227574 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 = 1.896227574 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = 1.896227574 + 1.388888889 x = 1.896227574 + 1.388888889 Combine like terms: 1.896227574 + 1.388888889 = 3.285116463 x = 3.285116463 Simplifying x = 3.285116463Subproblem 2
x + -1.388888889 = -1.896227574 Simplifying x + -1.388888889 = -1.896227574 Reorder the terms: -1.388888889 + x = -1.896227574 Solving -1.388888889 + x = -1.896227574 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 = -1.896227574 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = -1.896227574 + 1.388888889 x = -1.896227574 + 1.388888889 Combine like terms: -1.896227574 + 1.388888889 = -0.507338685 x = -0.507338685 Simplifying x = -0.507338685Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.285116463, -0.507338685}
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