A(w)=w^2+500w

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Solution for A(w)=w^2+500w equation:


Simplifying
A(w) = w2 + 500w

Multiply A * w
wA = w2 + 500w

Reorder the terms:
wA = 500w + w2

Solving
wA = 500w + w2

Solving for variable 'w'.

Reorder the terms:
-500w + wA + -1w2 = 500w + w2 + -500w + -1w2

Reorder the terms:
-500w + wA + -1w2 = 500w + -500w + w2 + -1w2

Combine like terms: 500w + -500w = 0
-500w + wA + -1w2 = 0 + w2 + -1w2
-500w + wA + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-500w + wA + -1w2 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(-500 + A + -1w) = 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 '(-500 + A + -1w)' equal to zero and attempt to solve: Simplifying -500 + A + -1w = 0 Solving -500 + A + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '500' to each side of the equation. -500 + A + 500 + -1w = 0 + 500 Reorder the terms: -500 + 500 + A + -1w = 0 + 500 Combine like terms: -500 + 500 = 0 0 + A + -1w = 0 + 500 A + -1w = 0 + 500 Combine like terms: 0 + 500 = 500 A + -1w = 500 Add '-1A' to each side of the equation. A + -1A + -1w = 500 + -1A Combine like terms: A + -1A = 0 0 + -1w = 500 + -1A -1w = 500 + -1A Divide each side by '-1'. w = -500 + A Simplifying w = -500 + A

Solution

w = {0, -500 + A}

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