Find the Roots (Zeros) P(I)=16I-0.04I^2

$P (I) = 16 I - 0.04 I^{2}$

Step 1

Set $16 I - 0.04 I^{2}$ equal to $0$ .

$16 I - 0.04 I^{2} = 0$

Step 2

Solve for $x$ .

Factor $0.04 I$ out of $16 I - 0.04 I^{2}$ .

Factor $0.04 I$ out of $16 I$ .

$0.04 I (400) - 0.04 I^{2} = 0$

Factor $0.04 I$ out of $- 0.04 I^{2}$ .

$0.04 I (400) + 0.04 I (- I) = 0$

Factor $0.04 I$ out of $0.04 I (400) + 0.04 I (- I)$ .

$0.04 I (400 - I) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$I = 0$

$400 - I = 0$

Set $I$ equal to $0$ .

$I = 0$

Set $400 - I$ equal to $0$ and solve for $I$ .

Set $400 - I$ equal to $0$ .

$400 - I = 0$

Solve $400 - I = 0$ for $I$ .

Subtract $400$ from both sides of the equation.

$- I = - 400$

Divide each term in $- I = - 400$ by $- 1$ and simplify.

Divide each term in $- I = - 400$ by $- 1$ .

$\frac{- I}{- 1} = \frac{- 400}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{I}{1} = \frac{- 400}{- 1}$

Divide $I$ by $1$ .

$I = \frac{- 400}{- 1}$

Simplify the right side.

Divide $- 400$ by $- 1$ .

$I = 400$

The final solution is all the values that make $0.04 I (400 - I) = 0$ true.

$I = 0, 400$

Step 3