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Simplifying 30 = w(w + 3) Reorder the terms: 30 = w(3 + w) 30 = (3 * w + w * w) 30 = (3w + w2) Solving 30 = 3w + w2 Solving for variable 'w'. Reorder the terms: 30 + -3w + -1w2 = 3w + -3w + w2 + -1w2 Combine like terms: 3w + -3w = 0 30 + -3w + -1w2 = 0 + w2 + -1w2 30 + -3w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 30 + -3w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + 3w + w2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 3w + 30 + w2 = 0 + 30 Reorder the terms: -30 + 30 + 3w + w2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 3w + w2 = 0 + 30 3w + w2 = 0 + 30 Combine like terms: 0 + 30 = 30 3w + w2 = 30 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 30 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 30 + 2.25 Combine like terms: 30 + 2.25 = 32.25 2.25 + 3w + w2 = 32.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (w + 1.5) equal to 5.678908346 and -5.678908346.Subproblem 1
w + 1.5 = 5.678908346 Simplifying w + 1.5 = 5.678908346 Reorder the terms: 1.5 + w = 5.678908346 Solving 1.5 + w = 5.678908346 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 5.678908346 + -1.5 w = 5.678908346 + -1.5 Combine like terms: 5.678908346 + -1.5 = 4.178908346 w = 4.178908346 Simplifying w = 4.178908346Subproblem 2
w + 1.5 = -5.678908346 Simplifying w + 1.5 = -5.678908346 Reorder the terms: 1.5 + w = -5.678908346 Solving 1.5 + w = -5.678908346 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -5.678908346 + -1.5 w = -5.678908346 + -1.5 Combine like terms: -5.678908346 + -1.5 = -7.178908346 w = -7.178908346 Simplifying w = -7.178908346Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.178908346, -7.178908346}
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