P(x)=60x-0.02x^2

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Solution for P(x)=60x-0.02x^2 equation:


Simplifying
P(x) = 60x + -0.02x2

Multiply P * x
xP = 60x + -0.02x2

Solving
xP = 60x + -0.02x2

Solving for variable 'x'.

Reorder the terms:
-60x + xP + 0.02x2 = 60x + -0.02x2 + -60x + 0.02x2

Reorder the terms:
-60x + xP + 0.02x2 = 60x + -60x + -0.02x2 + 0.02x2

Combine like terms: 60x + -60x = 0
-60x + xP + 0.02x2 = 0 + -0.02x2 + 0.02x2
-60x + xP + 0.02x2 = -0.02x2 + 0.02x2

Combine like terms: -0.02x2 + 0.02x2 = 0.00
-60x + xP + 0.02x2 = 0.00

Factor out the Greatest Common Factor (GCF), 'x'.
x(-60 + P + 0.02x) = 0.00

Subproblem 1

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

Subproblem 2

Set the factor '(-60 + P + 0.02x)' equal to zero and attempt to solve: Simplifying -60 + P + 0.02x = 0 Solving -60 + P + 0.02x = 0 Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + P + 60 + 0.02x = 0 + 60 Reorder the terms: -60 + 60 + P + 0.02x = 0 + 60 Combine like terms: -60 + 60 = 0 0 + P + 0.02x = 0 + 60 P + 0.02x = 0 + 60 Combine like terms: 0 + 60 = 60 P + 0.02x = 60 Add '-1P' to each side of the equation. P + -1P + 0.02x = 60 + -1P Combine like terms: P + -1P = 0 0 + 0.02x = 60 + -1P 0.02x = 60 + -1P Divide each side by '0.02'. x = 3000 + -50P Simplifying x = 3000 + -50P

Solution

x = {0, 3000 + -50P}

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