A(w)=-4w^2+80w

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Solution for A(w)=-4w^2+80w equation:


Simplifying
A(w) = -4w2 + 80w

Multiply A * w
wA = -4w2 + 80w

Reorder the terms:
wA = 80w + -4w2

Solving
wA = 80w + -4w2

Solving for variable 'w'.

Reorder the terms:
-80w + wA + 4w2 = 80w + -4w2 + -80w + 4w2

Reorder the terms:
-80w + wA + 4w2 = 80w + -80w + -4w2 + 4w2

Combine like terms: 80w + -80w = 0
-80w + wA + 4w2 = 0 + -4w2 + 4w2
-80w + wA + 4w2 = -4w2 + 4w2

Combine like terms: -4w2 + 4w2 = 0
-80w + wA + 4w2 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(-80 + A + 4w) = 0

Subproblem 1

Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0

Subproblem 2

Set the factor '(-80 + A + 4w)' equal to zero and attempt to solve: Simplifying -80 + A + 4w = 0 Solving -80 + A + 4w = 0 Move all terms containing w to the left, all other terms to the right. Add '80' to each side of the equation. -80 + A + 80 + 4w = 0 + 80 Reorder the terms: -80 + 80 + A + 4w = 0 + 80 Combine like terms: -80 + 80 = 0 0 + A + 4w = 0 + 80 A + 4w = 0 + 80 Combine like terms: 0 + 80 = 80 A + 4w = 80 Add '-1A' to each side of the equation. A + -1A + 4w = 80 + -1A Combine like terms: A + -1A = 0 0 + 4w = 80 + -1A 4w = 80 + -1A Divide each side by '4'. w = 20 + -0.25A Simplifying w = 20 + -0.25A

Solution

w = {0, 20 + -0.25A}

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