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Simplifying 18x2 + 50x + -25 = 0 Reorder the terms: -25 + 50x + 18x2 = 0 Solving -25 + 50x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -1.388888889 + 2.777777778x + x2 = 0 Move the constant term to the right: Add '1.388888889' to each side of the equation. -1.388888889 + 2.777777778x + 1.388888889 + x2 = 0 + 1.388888889 Reorder the terms: -1.388888889 + 1.388888889 + 2.777777778x + x2 = 0 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + 2.777777778x + x2 = 0 + 1.388888889 2.777777778x + x2 = 0 + 1.388888889 Combine like terms: 0 + 1.388888889 = 1.388888889 2.777777778x + x2 = 1.388888889 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 = 1.388888889 + 1.929012346 Reorder the terms: 1.929012346 + 2.777777778x + x2 = 1.388888889 + 1.929012346 Combine like terms: 1.388888889 + 1.929012346 = 3.317901235 1.929012346 + 2.777777778x + x2 = 3.317901235 Factor a perfect square on the left side: (x + 1.388888889)(x + 1.388888889) = 3.317901235 Calculate the square root of the right side: 1.821510701 Break this problem into two subproblems by setting (x + 1.388888889) equal to 1.821510701 and -1.821510701.Subproblem 1
x + 1.388888889 = 1.821510701 Simplifying x + 1.388888889 = 1.821510701 Reorder the terms: 1.388888889 + x = 1.821510701 Solving 1.388888889 + x = 1.821510701 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 = 1.821510701 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = 1.821510701 + -1.388888889 x = 1.821510701 + -1.388888889 Combine like terms: 1.821510701 + -1.388888889 = 0.432621812 x = 0.432621812 Simplifying x = 0.432621812Subproblem 2
x + 1.388888889 = -1.821510701 Simplifying x + 1.388888889 = -1.821510701 Reorder the terms: 1.388888889 + x = -1.821510701 Solving 1.388888889 + x = -1.821510701 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 = -1.821510701 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = -1.821510701 + -1.388888889 x = -1.821510701 + -1.388888889 Combine like terms: -1.821510701 + -1.388888889 = -3.21039959 x = -3.21039959 Simplifying x = -3.21039959Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.432621812, -3.21039959}
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