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Simplifying 12w(w + -3) = 480w3 Reorder the terms: 12w(-3 + w) = 480w3 (-3 * 12w + w * 12w) = 480w3 (-36w + 12w2) = 480w3 Solving -36w + 12w2 = 480w3 Solving for variable 'w'. Combine like terms: 480w3 + -480w3 = 0 -36w + 12w2 + -480w3 = 0 Factor out the Greatest Common Factor (GCF), '12w'. 12w(-3 + w + -40w2) = 0 Ignore the factor 12.Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(-3 + w + -40w2)' equal to zero and attempt to solve: Simplifying -3 + w + -40w2 = 0 Solving -3 + w + -40w2 = 0 Begin completing the square. Divide all terms by -40 the coefficient of the squared term: Divide each side by '-40'. 0.075 + -0.025w + w2 = 0.0 Move the constant term to the right: Add '-0.075' to each side of the equation. 0.075 + -0.025w + -0.075 + w2 = 0.0 + -0.075 Reorder the terms: 0.075 + -0.075 + -0.025w + w2 = 0.0 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + -0.025w + w2 = 0.0 + -0.075 -0.025w + w2 = 0.0 + -0.075 Combine like terms: 0.0 + -0.075 = -0.075 -0.025w + w2 = -0.075 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.025w + 0.25 + w2 = -0.075 + 0.25 Reorder the terms: 0.25 + -0.025w + w2 = -0.075 + 0.25 Combine like terms: -0.075 + 0.25 = 0.175 0.25 + -0.025w + w2 = 0.175 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 0.175 Calculate the square root of the right side: 0.418330013 Break this problem into two subproblems by setting (w + 0.5) equal to 0.418330013 and -0.418330013.Subproblem 1
w + 0.5 = 0.418330013 Simplifying w + 0.5 = 0.418330013 Reorder the terms: 0.5 + w = 0.418330013 Solving 0.5 + w = 0.418330013 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 0.418330013 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 0.418330013 + -0.5 w = 0.418330013 + -0.5 Combine like terms: 0.418330013 + -0.5 = -0.081669987 w = -0.081669987 Simplifying w = -0.081669987Subproblem 2
w + 0.5 = -0.418330013 Simplifying w + 0.5 = -0.418330013 Reorder the terms: 0.5 + w = -0.418330013 Solving 0.5 + w = -0.418330013 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -0.418330013 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -0.418330013 + -0.5 w = -0.418330013 + -0.5 Combine like terms: -0.418330013 + -0.5 = -0.918330013 w = -0.918330013 Simplifying w = -0.918330013Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.081669987, -0.918330013}Solution
w = {0, -0.081669987, -0.918330013}
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