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Simplifying 3w4 = 24w3 + 48w2 Reorder the terms: 3w4 = 48w2 + 24w3 Solving 3w4 = 48w2 + 24w3 Solving for variable 'w'. Reorder the terms: -48w2 + -24w3 + 3w4 = 48w2 + 24w3 + -48w2 + -24w3 Reorder the terms: -48w2 + -24w3 + 3w4 = 48w2 + -48w2 + 24w3 + -24w3 Combine like terms: 48w2 + -48w2 = 0 -48w2 + -24w3 + 3w4 = 0 + 24w3 + -24w3 -48w2 + -24w3 + 3w4 = 24w3 + -24w3 Combine like terms: 24w3 + -24w3 = 0 -48w2 + -24w3 + 3w4 = 0 Factor out the Greatest Common Factor (GCF), '3w2'. 3w2(-16 + -8w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve: Simplifying w2 = 0 Solving w2 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w2 = 0 Take the square root of each side: w = {0}Subproblem 2
Set the factor '(-16 + -8w + w2)' equal to zero and attempt to solve: Simplifying -16 + -8w + w2 = 0 Solving -16 + -8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -8w + 16 + w2 = 0 + 16 Reorder the terms: -16 + 16 + -8w + w2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -8w + w2 = 0 + 16 -8w + w2 = 0 + 16 Combine like terms: 0 + 16 = 16 -8w + w2 = 16 The w term is -8w. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8w + 16 + w2 = 16 + 16 Reorder the terms: 16 + -8w + w2 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + -8w + w2 = 32 Factor a perfect square on the left side: (w + -4)(w + -4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (w + -4) equal to 5.656854249 and -5.656854249.Subproblem 1
w + -4 = 5.656854249 Simplifying w + -4 = 5.656854249 Reorder the terms: -4 + w = 5.656854249 Solving -4 + w = 5.656854249 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + w = 5.656854249 + 4 w = 5.656854249 + 4 Combine like terms: 5.656854249 + 4 = 9.656854249 w = 9.656854249 Simplifying w = 9.656854249Subproblem 2
w + -4 = -5.656854249 Simplifying w + -4 = -5.656854249 Reorder the terms: -4 + w = -5.656854249 Solving -4 + w = -5.656854249 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = -5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + w = -5.656854249 + 4 w = -5.656854249 + 4 Combine like terms: -5.656854249 + 4 = -1.656854249 w = -1.656854249 Simplifying w = -1.656854249Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.656854249, -1.656854249}Solution
w = {0, 9.656854249, -1.656854249}
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