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Simplifying 46 = 3w2 + 3w Reorder the terms: 46 = 3w + 3w2 Solving 46 = 3w + 3w2 Solving for variable 'w'. Reorder the terms: 46 + -3w + -3w2 = 3w + -3w + 3w2 + -3w2 Combine like terms: 3w + -3w = 0 46 + -3w + -3w2 = 0 + 3w2 + -3w2 46 + -3w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 46 + -3w + -3w2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -15.33333333 + w + w2 = 0 Move the constant term to the right: Add '15.33333333' to each side of the equation. -15.33333333 + w + 15.33333333 + w2 = 0 + 15.33333333 Reorder the terms: -15.33333333 + 15.33333333 + w + w2 = 0 + 15.33333333 Combine like terms: -15.33333333 + 15.33333333 = 0.00000000 0.00000000 + w + w2 = 0 + 15.33333333 w + w2 = 0 + 15.33333333 Combine like terms: 0 + 15.33333333 = 15.33333333 w + w2 = 15.33333333 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. + 0.25 + w2 = 15.33333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + w2 = 15.33333333 + 0.25 Combine like terms: 15.33333333 + 0.25 = 15.58333333 1.25 + w2 = 15.58333333 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 15.58333333 Calculate the square root of the right side: 3.947573094 Break this problem into two subproblems by setting (w + 0.5) equal to 3.947573094 and -3.947573094.Subproblem 1
w + 0.5 = 3.947573094 Simplifying w + 0.5 = 3.947573094 Reorder the terms: 0.5 + w = 3.947573094 Solving 0.5 + w = 3.947573094 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 = 3.947573094 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 3.947573094 + -0.5 w = 3.947573094 + -0.5 Combine like terms: 3.947573094 + -0.5 = 3.447573094 w = 3.447573094 Simplifying w = 3.447573094Subproblem 2
w + 0.5 = -3.947573094 Simplifying w + 0.5 = -3.947573094 Reorder the terms: 0.5 + w = -3.947573094 Solving 0.5 + w = -3.947573094 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 = -3.947573094 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -3.947573094 + -0.5 w = -3.947573094 + -0.5 Combine like terms: -3.947573094 + -0.5 = -4.447573094 w = -4.447573094 Simplifying w = -4.447573094Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.447573094, -4.447573094}
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