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Simplifying 6w(5w2 + -5w + 5) = 0 Reorder the terms: 6w(5 + -5w + 5w2) = 0 (5 * 6w + -5w * 6w + 5w2 * 6w) = 0 (30w + -30w2 + 30w3) = 0 Solving 30w + -30w2 + 30w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '30w'. 30w(1 + -1w + w2) = 0 Ignore the factor 30.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 '(1 + -1w + w2)' equal to zero and attempt to solve: Simplifying 1 + -1w + w2 = 0 Solving 1 + -1w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1w + -1 + w2 = 0 + -1 Reorder the terms: 1 + -1 + -1w + w2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w + w2 = 0 + -1 -1w + w2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1w + w2 = -1 The w term is -1w. 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. -1w + 0.25 + w2 = -1 + 0.25 Reorder the terms: 0.25 + -1w + w2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -1w + w2 = -0.75 Factor a perfect square on the left side: (w + -0.5)(w + -0.5) = -0.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
w = {0}
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