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Simplifying 3w2 + 30w = 7 Reorder the terms: 30w + 3w2 = 7 Solving 30w + 3w2 = 7 Solving for variable 'w'. Reorder the terms: -7 + 30w + 3w2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 30w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + 10w + w2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 10w + 2.333333333 + w2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 10w + w2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 10w + w2 = 0 + 2.333333333 10w + w2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 10w + w2 = 2.333333333 The w term is 10w. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10w + 25 + w2 = 2.333333333 + 25 Reorder the terms: 25 + 10w + w2 = 2.333333333 + 25 Combine like terms: 2.333333333 + 25 = 27.333333333 25 + 10w + w2 = 27.333333333 Factor a perfect square on the left side: (w + 5)(w + 5) = 27.333333333 Calculate the square root of the right side: 5.228129047 Break this problem into two subproblems by setting (w + 5) equal to 5.228129047 and -5.228129047.Subproblem 1
w + 5 = 5.228129047 Simplifying w + 5 = 5.228129047 Reorder the terms: 5 + w = 5.228129047 Solving 5 + w = 5.228129047 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 5.228129047 + -5 Combine like terms: 5 + -5 = 0 0 + w = 5.228129047 + -5 w = 5.228129047 + -5 Combine like terms: 5.228129047 + -5 = 0.228129047 w = 0.228129047 Simplifying w = 0.228129047Subproblem 2
w + 5 = -5.228129047 Simplifying w + 5 = -5.228129047 Reorder the terms: 5 + w = -5.228129047 Solving 5 + w = -5.228129047 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = -5.228129047 + -5 Combine like terms: 5 + -5 = 0 0 + w = -5.228129047 + -5 w = -5.228129047 + -5 Combine like terms: -5.228129047 + -5 = -10.228129047 w = -10.228129047 Simplifying w = -10.228129047Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.228129047, -10.228129047}
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