Question

Age of x equals negative 1/2 x (x-20)

Answer 1

To solve the equation \( x = -\frac{1}{2} x (x - 20) \), we start by simplifying it.

1. Distribute the \(-\frac{1}{2} x\):
\[
x = -\frac{1}{2} x^2 + 10x
\]

2. Rearranging the equation to bring all terms to one side gives:
\[
\frac{1}{2} x^2 - 10x + x = 0
\]
Simplifying further:
\[
\frac{1}{2} x^2 - 9x = 0
\]

3. Factor the equation:
\[
x(\frac{1}{2} x - 9) = 0
\]

4. Setting each factor to zero gives:
\[
x = 0 \quad \text{or} \quad \frac{1}{2} x - 9 = 0
\]

5. From the second factor, solve for \( x \):
\[
\frac{1}{2} x = 9
\]
\[
x = 18
\]

Therefore, the solutions are:
\[
x = 0 \quad \text{or} \quad x = 18
\]

So, the values of \( x \) that satisfy the equation are \( x = 0 \) and \( x = 18 \).