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Simplifying 3w2 + 16w = 864 Reorder the terms: 16w + 3w2 = 864 Solving 16w + 3w2 = 864 Solving for variable 'w'. Reorder the terms: -864 + 16w + 3w2 = 864 + -864 Combine like terms: 864 + -864 = 0 -864 + 16w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -288 + 5.333333333w + w2 = 0 Move the constant term to the right: Add '288' to each side of the equation. -288 + 5.333333333w + 288 + w2 = 0 + 288 Reorder the terms: -288 + 288 + 5.333333333w + w2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + 5.333333333w + w2 = 0 + 288 5.333333333w + w2 = 0 + 288 Combine like terms: 0 + 288 = 288 5.333333333w + w2 = 288 The w term is 5.333333333w. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333w + 7.111111113 + w2 = 288 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333w + w2 = 288 + 7.111111113 Combine like terms: 288 + 7.111111113 = 295.111111113 7.111111113 + 5.333333333w + w2 = 295.111111113 Factor a perfect square on the left side: (w + 2.666666667)(w + 2.666666667) = 295.111111113 Calculate the square root of the right side: 17.178798302 Break this problem into two subproblems by setting (w + 2.666666667) equal to 17.178798302 and -17.178798302.Subproblem 1
w + 2.666666667 = 17.178798302 Simplifying w + 2.666666667 = 17.178798302 Reorder the terms: 2.666666667 + w = 17.178798302 Solving 2.666666667 + w = 17.178798302 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + w = 17.178798302 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + w = 17.178798302 + -2.666666667 w = 17.178798302 + -2.666666667 Combine like terms: 17.178798302 + -2.666666667 = 14.512131635 w = 14.512131635 Simplifying w = 14.512131635Subproblem 2
w + 2.666666667 = -17.178798302 Simplifying w + 2.666666667 = -17.178798302 Reorder the terms: 2.666666667 + w = -17.178798302 Solving 2.666666667 + w = -17.178798302 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + w = -17.178798302 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + w = -17.178798302 + -2.666666667 w = -17.178798302 + -2.666666667 Combine like terms: -17.178798302 + -2.666666667 = -19.845464969 w = -19.845464969 Simplifying w = -19.845464969Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.512131635, -19.845464969}
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