I(x)=-3x^2+3000x

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Solution for I(x)=-3x^2+3000x equation:


Simplifying
I(x) = -3x2 + 3000x

Multiply I * x
xI = -3x2 + 3000x

Reorder the terms:
xI = 3000x + -3x2

Solving
xI = 3000x + -3x2

Solving for variable 'x'.

Reorder the terms:
-3000x + xI + 3x2 = 3000x + -3x2 + -3000x + 3x2

Reorder the terms:
-3000x + xI + 3x2 = 3000x + -3000x + -3x2 + 3x2

Combine like terms: 3000x + -3000x = 0
-3000x + xI + 3x2 = 0 + -3x2 + 3x2
-3000x + xI + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-3000x + xI + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3000 + I + 3x) = 0

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 '(-3000 + I + 3x)' equal to zero and attempt to solve: Simplifying -3000 + I + 3x = 0 Solving -3000 + I + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '3000' to each side of the equation. -3000 + I + 3000 + 3x = 0 + 3000 Reorder the terms: -3000 + 3000 + I + 3x = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + I + 3x = 0 + 3000 I + 3x = 0 + 3000 Combine like terms: 0 + 3000 = 3000 I + 3x = 3000 Add '-1I' to each side of the equation. I + -1I + 3x = 3000 + -1I Combine like terms: I + -1I = 0 0 + 3x = 3000 + -1I 3x = 3000 + -1I Divide each side by '3'. x = 1000 + -0.3333333333I Simplifying x = 1000 + -0.3333333333I

Solution

x = {0, 1000 + -0.3333333333I}

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