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Simplifying 4w4 = 40w2 + -44 Reorder the terms: 4w4 = -44 + 40w2 Solving 4w4 = -44 + 40w2 Solving for variable 'w'. Reorder the terms: 44 + -40w2 + 4w4 = -44 + 40w2 + 44 + -40w2 Reorder the terms: 44 + -40w2 + 4w4 = -44 + 44 + 40w2 + -40w2 Combine like terms: -44 + 44 = 0 44 + -40w2 + 4w4 = 0 + 40w2 + -40w2 44 + -40w2 + 4w4 = 40w2 + -40w2 Combine like terms: 40w2 + -40w2 = 0 44 + -40w2 + 4w4 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(11 + -10w2 + w4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(11 + -10w2 + w4)' equal to zero and attempt to solve: Simplifying 11 + -10w2 + w4 = 0 Solving 11 + -10w2 + w4 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -10w2 + -11 + w4 = 0 + -11 Reorder the terms: 11 + -11 + -10w2 + w4 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -10w2 + w4 = 0 + -11 -10w2 + w4 = 0 + -11 Combine like terms: 0 + -11 = -11 -10w2 + w4 = -11 The w term is -10w2. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10w2 + 25 + w4 = -11 + 25 Reorder the terms: 25 + -10w2 + w4 = -11 + 25 Combine like terms: -11 + 25 = 14 25 + -10w2 + w4 = 14 Factor a perfect square on the left side: (w2 + -5)(w2 + -5) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (w2 + -5) equal to 3.741657387 and -3.741657387.Subproblem 1
w2 + -5 = 3.741657387 Simplifying w2 + -5 = 3.741657387 Reorder the terms: -5 + w2 = 3.741657387 Solving -5 + w2 = 3.741657387 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w2 = 3.741657387 + 5 Combine like terms: -5 + 5 = 0 0 + w2 = 3.741657387 + 5 w2 = 3.741657387 + 5 Combine like terms: 3.741657387 + 5 = 8.741657387 w2 = 8.741657387 Simplifying w2 = 8.741657387 Take the square root of each side: w = {-2.956629396, 2.956629396}Subproblem 2
w2 + -5 = -3.741657387 Simplifying w2 + -5 = -3.741657387 Reorder the terms: -5 + w2 = -3.741657387 Solving -5 + w2 = -3.741657387 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w2 = -3.741657387 + 5 Combine like terms: -5 + 5 = 0 0 + w2 = -3.741657387 + 5 w2 = -3.741657387 + 5 Combine like terms: -3.741657387 + 5 = 1.258342613 w2 = 1.258342613 Simplifying w2 = 1.258342613 Take the square root of each side: w = {-1.121758714, 1.121758714}Solution
The solution to the problem is based on the solutions from the subproblems. w = {-2.956629396, 2.956629396, -1.121758714, 1.121758714}Solution
w = {-2.956629396, 2.956629396, -1.121758714, 1.121758714}
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