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Simplifying 30w = 9w2 + 25 Reorder the terms: 30w = 25 + 9w2 Solving 30w = 25 + 9w2 Solving for variable 'w'. Reorder the terms: -25 + 30w + -9w2 = 25 + 9w2 + -25 + -9w2 Reorder the terms: -25 + 30w + -9w2 = 25 + -25 + 9w2 + -9w2 Combine like terms: 25 + -25 = 0 -25 + 30w + -9w2 = 0 + 9w2 + -9w2 -25 + 30w + -9w2 = 9w2 + -9w2 Combine like terms: 9w2 + -9w2 = 0 -25 + 30w + -9w2 = 0 Factor a trinomial. (-5 + 3w)(5 + -3w) = 0Subproblem 1
Set the factor '(-5 + 3w)' equal to zero and attempt to solve: Simplifying -5 + 3w = 0 Solving -5 + 3w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 3w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3w = 0 + 5 3w = 0 + 5 Combine like terms: 0 + 5 = 5 3w = 5 Divide each side by '3'. w = 1.666666667 Simplifying w = 1.666666667Subproblem 2
Set the factor '(5 + -3w)' equal to zero and attempt to solve: Simplifying 5 + -3w = 0 Solving 5 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3w = 0 + -5 -3w = 0 + -5 Combine like terms: 0 + -5 = -5 -3w = -5 Divide each side by '-3'. w = 1.666666667 Simplifying w = 1.666666667Solution
w = {1.666666667, 1.666666667}
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