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Simplifying 3w2 + -15w + -28 = 0 Reorder the terms: -28 + -15w + 3w2 = 0 Solving -28 + -15w + 3w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9.333333333 + -5w + w2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -5w + 9.333333333 + w2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -5w + w2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -5w + w2 = 0 + 9.333333333 -5w + w2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -5w + w2 = 9.333333333 The w term is -5w. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5w + 6.25 + w2 = 9.333333333 + 6.25 Reorder the terms: 6.25 + -5w + w2 = 9.333333333 + 6.25 Combine like terms: 9.333333333 + 6.25 = 15.583333333 6.25 + -5w + w2 = 15.583333333 Factor a perfect square on the left side: (w + -2.5)(w + -2.5) = 15.583333333 Calculate the square root of the right side: 3.947573094 Break this problem into two subproblems by setting (w + -2.5) equal to 3.947573094 and -3.947573094.Subproblem 1
w + -2.5 = 3.947573094 Simplifying w + -2.5 = 3.947573094 Reorder the terms: -2.5 + w = 3.947573094 Solving -2.5 + w = 3.947573094 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + w = 3.947573094 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + w = 3.947573094 + 2.5 w = 3.947573094 + 2.5 Combine like terms: 3.947573094 + 2.5 = 6.447573094 w = 6.447573094 Simplifying w = 6.447573094Subproblem 2
w + -2.5 = -3.947573094 Simplifying w + -2.5 = -3.947573094 Reorder the terms: -2.5 + w = -3.947573094 Solving -2.5 + w = -3.947573094 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + w = -3.947573094 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + w = -3.947573094 + 2.5 w = -3.947573094 + 2.5 Combine like terms: -3.947573094 + 2.5 = -1.447573094 w = -1.447573094 Simplifying w = -1.447573094Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.447573094, -1.447573094}
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