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Simplifying 0 = 3w2 + -400w + 10000 Reorder the terms: 0 = 10000 + -400w + 3w2 Solving 0 = 10000 + -400w + 3w2 Solving for variable 'w'. Combine like terms: 0 + -10000 = -10000 -10000 + 400w + -3w2 = 10000 + -400w + 3w2 + -10000 + 400w + -3w2 Reorder the terms: -10000 + 400w + -3w2 = 10000 + -10000 + -400w + 400w + 3w2 + -3w2 Combine like terms: 10000 + -10000 = 0 -10000 + 400w + -3w2 = 0 + -400w + 400w + 3w2 + -3w2 -10000 + 400w + -3w2 = -400w + 400w + 3w2 + -3w2 Combine like terms: -400w + 400w = 0 -10000 + 400w + -3w2 = 0 + 3w2 + -3w2 -10000 + 400w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 -10000 + 400w + -3w2 = 0 Factor a trinomial. (-100 + w)(100 + -3w) = 0Subproblem 1
Set the factor '(-100 + w)' equal to zero and attempt to solve: Simplifying -100 + w = 0 Solving -100 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + w = 0 + 100 Combine like terms: -100 + 100 = 0 0 + w = 0 + 100 w = 0 + 100 Combine like terms: 0 + 100 = 100 w = 100 Simplifying w = 100Subproblem 2
Set the factor '(100 + -3w)' equal to zero and attempt to solve: Simplifying 100 + -3w = 0 Solving 100 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + -3w = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -3w = 0 + -100 -3w = 0 + -100 Combine like terms: 0 + -100 = -100 -3w = -100 Divide each side by '-3'. w = 33.33333333 Simplifying w = 33.33333333Solution
w = {100, 33.33333333}
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