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Simplifying 9x2 + -25x + 12 = 0 Reorder the terms: 12 + -25x + 9x2 = 0 Solving 12 + -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'. 1.333333333 + -2.777777778x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -2.777777778x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -2.777777778x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -2.777777778x + x2 = 0 + -1.333333333 -2.777777778x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -2.777777778x + x2 = -1.333333333 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 = -1.333333333 + 1.929012346 Reorder the terms: 1.929012346 + -2.777777778x + x2 = -1.333333333 + 1.929012346 Combine like terms: -1.333333333 + 1.929012346 = 0.595679013 1.929012346 + -2.777777778x + x2 = 0.595679013 Factor a perfect square on the left side: (x + -1.388888889)(x + -1.388888889) = 0.595679013 Calculate the square root of the right side: 0.771802444 Break this problem into two subproblems by setting (x + -1.388888889) equal to 0.771802444 and -0.771802444.Subproblem 1
x + -1.388888889 = 0.771802444 Simplifying x + -1.388888889 = 0.771802444 Reorder the terms: -1.388888889 + x = 0.771802444 Solving -1.388888889 + x = 0.771802444 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 = 0.771802444 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = 0.771802444 + 1.388888889 x = 0.771802444 + 1.388888889 Combine like terms: 0.771802444 + 1.388888889 = 2.160691333 x = 2.160691333 Simplifying x = 2.160691333Subproblem 2
x + -1.388888889 = -0.771802444 Simplifying x + -1.388888889 = -0.771802444 Reorder the terms: -1.388888889 + x = -0.771802444 Solving -1.388888889 + x = -0.771802444 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 = -0.771802444 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = -0.771802444 + 1.388888889 x = -0.771802444 + 1.388888889 Combine like terms: -0.771802444 + 1.388888889 = 0.617086445 x = 0.617086445 Simplifying x = 0.617086445Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.160691333, 0.617086445}
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