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Simplifying 9w4 + -81w2 + 153 = 0 Reorder the terms: 153 + -81w2 + 9w4 = 0 Solving 153 + -81w2 + 9w4 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '9'. 9(17 + -9w2 + w4) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(17 + -9w2 + w4)' equal to zero and attempt to solve: Simplifying 17 + -9w2 + w4 = 0 Solving 17 + -9w2 + w4 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -9w2 + -17 + w4 = 0 + -17 Reorder the terms: 17 + -17 + -9w2 + w4 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -9w2 + w4 = 0 + -17 -9w2 + w4 = 0 + -17 Combine like terms: 0 + -17 = -17 -9w2 + w4 = -17 The w term is -9w2. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9w2 + 20.25 + w4 = -17 + 20.25 Reorder the terms: 20.25 + -9w2 + w4 = -17 + 20.25 Combine like terms: -17 + 20.25 = 3.25 20.25 + -9w2 + w4 = 3.25 Factor a perfect square on the left side: (w2 + -4.5)(w2 + -4.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (w2 + -4.5) equal to 1.802775638 and -1.802775638.Subproblem 1
w2 + -4.5 = 1.802775638 Simplifying w2 + -4.5 = 1.802775638 Reorder the terms: -4.5 + w2 = 1.802775638 Solving -4.5 + w2 = 1.802775638 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + w2 = 1.802775638 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w2 = 1.802775638 + 4.5 w2 = 1.802775638 + 4.5 Combine like terms: 1.802775638 + 4.5 = 6.302775638 w2 = 6.302775638 Simplifying w2 = 6.302775638 Take the square root of each side: w = {-2.510532939, 2.510532939}Subproblem 2
w2 + -4.5 = -1.802775638 Simplifying w2 + -4.5 = -1.802775638 Reorder the terms: -4.5 + w2 = -1.802775638 Solving -4.5 + w2 = -1.802775638 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + w2 = -1.802775638 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w2 = -1.802775638 + 4.5 w2 = -1.802775638 + 4.5 Combine like terms: -1.802775638 + 4.5 = 2.697224362 w2 = 2.697224362 Simplifying w2 = 2.697224362 Take the square root of each side: w = {-1.642322856, 1.642322856}Solution
The solution to the problem is based on the solutions from the subproblems. w = {-2.510532939, 2.510532939, -1.642322856, 1.642322856}Solution
w = {-2.510532939, 2.510532939, -1.642322856, 1.642322856}
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