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Simplifying (3x)(3x) + 25x + -18 = 0 Remove parenthesis around (3x) 3x(3x) + 25x + -18 = 0 Remove parenthesis around (3x) 3x * 3x + 25x + -18 = 0 Reorder the terms for easier multiplication: 3 * 3x * x + 25x + -18 = 0 Multiply 3 * 3 9x * x + 25x + -18 = 0 Multiply x * x 9x2 + 25x + -18 = 0 Reorder the terms: -18 + 25x + 9x2 = 0 Solving -18 + 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 + 2.777777778x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.777777778x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 2.777777778x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.777777778x + x2 = 0 + 2 2.777777778x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.777777778x + x2 = 2 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 + 1.929012346 Reorder the terms: 1.929012346 + 2.777777778x + x2 = 2 + 1.929012346 Combine like terms: 2 + 1.929012346 = 3.929012346 1.929012346 + 2.777777778x + x2 = 3.929012346 Factor a perfect square on the left side: (x + 1.388888889)(x + 1.388888889) = 3.929012346 Calculate the square root of the right side: 1.982173642 Break this problem into two subproblems by setting (x + 1.388888889) equal to 1.982173642 and -1.982173642.Subproblem 1
x + 1.388888889 = 1.982173642 Simplifying x + 1.388888889 = 1.982173642 Reorder the terms: 1.388888889 + x = 1.982173642 Solving 1.388888889 + x = 1.982173642 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 = 1.982173642 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = 1.982173642 + -1.388888889 x = 1.982173642 + -1.388888889 Combine like terms: 1.982173642 + -1.388888889 = 0.593284753 x = 0.593284753 Simplifying x = 0.593284753Subproblem 2
x + 1.388888889 = -1.982173642 Simplifying x + 1.388888889 = -1.982173642 Reorder the terms: 1.388888889 + x = -1.982173642 Solving 1.388888889 + x = -1.982173642 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 = -1.982173642 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = -1.982173642 + -1.388888889 x = -1.982173642 + -1.388888889 Combine like terms: -1.982173642 + -1.388888889 = -3.371062531 x = -3.371062531 Simplifying x = -3.371062531Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.593284753, -3.371062531}
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