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Simplifying 2w(-2w2 + 19w + 2) = 0 Reorder the terms: 2w(2 + 19w + -2w2) = 0 (2 * 2w + 19w * 2w + -2w2 * 2w) = 0 (4w + 38w2 + -4w3) = 0 Solving 4w + 38w2 + -4w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w'. 2w(2 + 19w + -2w2) = 0 Ignore the factor 2.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 '(2 + 19w + -2w2)' equal to zero and attempt to solve: Simplifying 2 + 19w + -2w2 = 0 Solving 2 + 19w + -2w2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + -9.5w + w2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -9.5w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + -9.5w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -9.5w + w2 = 0 + 1 -9.5w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 -9.5w + w2 = 1 The w term is -9.5w. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5w + 22.5625 + w2 = 1 + 22.5625 Reorder the terms: 22.5625 + -9.5w + w2 = 1 + 22.5625 Combine like terms: 1 + 22.5625 = 23.5625 22.5625 + -9.5w + w2 = 23.5625 Factor a perfect square on the left side: (w + -4.75)(w + -4.75) = 23.5625 Calculate the square root of the right side: 4.85412196 Break this problem into two subproblems by setting (w + -4.75) equal to 4.85412196 and -4.85412196.Subproblem 1
w + -4.75 = 4.85412196 Simplifying w + -4.75 = 4.85412196 Reorder the terms: -4.75 + w = 4.85412196 Solving -4.75 + w = 4.85412196 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + w = 4.85412196 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + w = 4.85412196 + 4.75 w = 4.85412196 + 4.75 Combine like terms: 4.85412196 + 4.75 = 9.60412196 w = 9.60412196 Simplifying w = 9.60412196Subproblem 2
w + -4.75 = -4.85412196 Simplifying w + -4.75 = -4.85412196 Reorder the terms: -4.75 + w = -4.85412196 Solving -4.75 + w = -4.85412196 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + w = -4.85412196 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + w = -4.85412196 + 4.75 w = -4.85412196 + 4.75 Combine like terms: -4.85412196 + 4.75 = -0.10412196 w = -0.10412196 Simplifying w = -0.10412196Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.60412196, -0.10412196}Solution
w = {0, 9.60412196, -0.10412196}
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