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Simplifying 9x2 + 25x + -24 = 0 Reorder the terms: -24 + 25x + 9x2 = 0 Solving -24 + 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'. -2.666666667 + 2.777777778x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 2.777777778x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 2.777777778x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 2.777777778x + x2 = 0 + 2.666666667 2.777777778x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 2.777777778x + x2 = 2.666666667 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 = 2.666666667 + 1.929012346 Reorder the terms: 1.929012346 + 2.777777778x + x2 = 2.666666667 + 1.929012346 Combine like terms: 2.666666667 + 1.929012346 = 4.595679013 1.929012346 + 2.777777778x + x2 = 4.595679013 Factor a perfect square on the left side: (x + 1.388888889)(x + 1.388888889) = 4.595679013 Calculate the square root of the right side: 2.143753487 Break this problem into two subproblems by setting (x + 1.388888889) equal to 2.143753487 and -2.143753487.Subproblem 1
x + 1.388888889 = 2.143753487 Simplifying x + 1.388888889 = 2.143753487 Reorder the terms: 1.388888889 + x = 2.143753487 Solving 1.388888889 + x = 2.143753487 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 = 2.143753487 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = 2.143753487 + -1.388888889 x = 2.143753487 + -1.388888889 Combine like terms: 2.143753487 + -1.388888889 = 0.754864598 x = 0.754864598 Simplifying x = 0.754864598Subproblem 2
x + 1.388888889 = -2.143753487 Simplifying x + 1.388888889 = -2.143753487 Reorder the terms: 1.388888889 + x = -2.143753487 Solving 1.388888889 + x = -2.143753487 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 = -2.143753487 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = -2.143753487 + -1.388888889 x = -2.143753487 + -1.388888889 Combine like terms: -2.143753487 + -1.388888889 = -3.532642376 x = -3.532642376 Simplifying x = -3.532642376Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.754864598, -3.532642376}
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