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Simplifying (30 + w) + -1(5 + w) * w = 0 Remove parenthesis around (30 + w) 30 + w + -1(5 + w) * w = 0 Reorder the terms for easier multiplication: 30 + w + -1w(5 + w) = 0 30 + w + (5 * -1w + w * -1w) = 0 30 + w + (-5w + -1w2) = 0 Combine like terms: w + -5w = -4w 30 + -4w + -1w2 = 0 Solving 30 + -4w + -1w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + 4w + w2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 4w + 30 + w2 = 0 + 30 Reorder the terms: -30 + 30 + 4w + w2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 4w + w2 = 0 + 30 4w + w2 = 0 + 30 Combine like terms: 0 + 30 = 30 4w + w2 = 30 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 30 + 4 Reorder the terms: 4 + 4w + w2 = 30 + 4 Combine like terms: 30 + 4 = 34 4 + 4w + w2 = 34 Factor a perfect square on the left side: (w + 2)(w + 2) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (w + 2) equal to 5.830951895 and -5.830951895.Subproblem 1
w + 2 = 5.830951895 Simplifying w + 2 = 5.830951895 Reorder the terms: 2 + w = 5.830951895 Solving 2 + w = 5.830951895 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + w = 5.830951895 + -2 w = 5.830951895 + -2 Combine like terms: 5.830951895 + -2 = 3.830951895 w = 3.830951895 Simplifying w = 3.830951895Subproblem 2
w + 2 = -5.830951895 Simplifying w + 2 = -5.830951895 Reorder the terms: 2 + w = -5.830951895 Solving 2 + w = -5.830951895 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + w = -5.830951895 + -2 w = -5.830951895 + -2 Combine like terms: -5.830951895 + -2 = -7.830951895 w = -7.830951895 Simplifying w = -7.830951895Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.830951895, -7.830951895}
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