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Simplifying -9w2 + -25w + -10 = 0 Reorder the terms: -10 + -25w + -9w2 = 0 Solving -10 + -25w + -9w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 25w + 9w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 25w + 9w2)' equal to zero and attempt to solve: Simplifying 10 + 25w + 9w2 = 0 Solving 10 + 25w + 9w2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.111111111 + 2.777777778w + w2 = 0 Move the constant term to the right: Add '-1.111111111' to each side of the equation. 1.111111111 + 2.777777778w + -1.111111111 + w2 = 0 + -1.111111111 Reorder the terms: 1.111111111 + -1.111111111 + 2.777777778w + w2 = 0 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + 2.777777778w + w2 = 0 + -1.111111111 2.777777778w + w2 = 0 + -1.111111111 Combine like terms: 0 + -1.111111111 = -1.111111111 2.777777778w + w2 = -1.111111111 The w term is 2.777777778w. 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. 2.777777778w + 1.929012346 + w2 = -1.111111111 + 1.929012346 Reorder the terms: 1.929012346 + 2.777777778w + w2 = -1.111111111 + 1.929012346 Combine like terms: -1.111111111 + 1.929012346 = 0.817901235 1.929012346 + 2.777777778w + w2 = 0.817901235 Factor a perfect square on the left side: (w + 1.388888889)(w + 1.388888889) = 0.817901235 Calculate the square root of the right side: 0.904378922 Break this problem into two subproblems by setting (w + 1.388888889) equal to 0.904378922 and -0.904378922.Subproblem 1
w + 1.388888889 = 0.904378922 Simplifying w + 1.388888889 = 0.904378922 Reorder the terms: 1.388888889 + w = 0.904378922 Solving 1.388888889 + w = 0.904378922 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.388888889' to each side of the equation. 1.388888889 + -1.388888889 + w = 0.904378922 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + w = 0.904378922 + -1.388888889 w = 0.904378922 + -1.388888889 Combine like terms: 0.904378922 + -1.388888889 = -0.484509967 w = -0.484509967 Simplifying w = -0.484509967Subproblem 2
w + 1.388888889 = -0.904378922 Simplifying w + 1.388888889 = -0.904378922 Reorder the terms: 1.388888889 + w = -0.904378922 Solving 1.388888889 + w = -0.904378922 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.388888889' to each side of the equation. 1.388888889 + -1.388888889 + w = -0.904378922 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + w = -0.904378922 + -1.388888889 w = -0.904378922 + -1.388888889 Combine like terms: -0.904378922 + -1.388888889 = -2.293267811 w = -2.293267811 Simplifying w = -2.293267811Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.484509967, -2.293267811}Solution
w = {-0.484509967, -2.293267811}
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