Solve for x 1599=16x-0.04x^2

$1599 = 16 x - 0.04 x^{2}$

Step 1

Rewrite the equation as $16 x - 0.04 x^{2} = 1599$ .

$16 x - 0.04 x^{2} = 1599$

Step 2

Subtract $1599$ from both sides of the equation.

$16 x - 0.04 x^{2} - 1599 = 0$

Step 3

Factor the left side of the equation.

Factor $- 0.04$ out of $16 x - 0.04 x^{2} - 1599$ .

Reorder $16 x$ and $- 0.04 x^{2}$ .

$- 0.04 x^{2} + 16 x - 1599 = 0$

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

$- 0.04 x^{2} + 16 x - 1599 = 0$

Factor $- 0.04$ out of $16 x$ .

$- 0.04 x^{2} - 0.04 (- 400 x) - 1599 = 0$

Factor $- 0.04$ out of $- 1599$ .

$- 0.04 x^{2} - 0.04 (- 400 x) - 0.04 \cdot 39975 = 0$

Factor $- 0.04$ out of $- 0.04 (x^{2}) - 0.04 (- 400 x)$ .

$- 0.04 (x^{2} - 400 x) - 0.04 \cdot 39975 = 0$

Factor $- 0.04$ out of $- 0.04 (x^{2} - 400 x) - 0.04 (39975)$ .

$- 0.04 (x^{2} - 400 x + 39975) = 0$

Factor.

Factor $x^{2} - 400 x + 39975$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $39975$ and whose sum is $- 400$ .

$- 205, - 195$

Write the factored form using these integers.

$- 0.04 ((x - 205) (x - 195)) = 0$

Remove unnecessary parentheses.

$- 0.04 (x - 205) (x - 195) = 0$

Step 4

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

$x - 205 = 0$

$x - 195 = 0$

Step 5

Set $x - 205$ equal to $0$ and solve for $x$ .

Set $x - 205$ equal to $0$ .

$x - 205 = 0$

Add $205$ to both sides of the equation.

$x = 205$

Step 6

Set $x - 195$ equal to $0$ and solve for $x$ .

Set $x - 195$ equal to $0$ .

$x - 195 = 0$

Add $195$ to both sides of the equation.

$x = 195$

Step 7

The final solution is all the values that make $- 0.04 (x - 205) (x - 195) = 0$ true.

$x = 205, 195$

Solve for x 1599=16x-0.04x^2

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