Final answer:
The equation 2x - x² = 18x is rearranged to the standard quadratic form x² - 20x = 0. Factoring out x gives x(x - 20) = 0, with solutions x = 0 and x = 20.
Step-by-step explanation:
To solve the equation for x: 2x - x² = 18x, first we need to arrange the equation into a standard quadratic form ax² + bx + c = 0. We do this by subtracting 18x from both sides of the equation, yielding:
x² - 20x = 0
Now, we can factor out an x from the left side of the equation:
x(x - 20) = 0
Setting each factor equal to zero gives us two possible solutions for x:
- x = 0
- x - 20 = 0, which simplifies to x = 20
Therefore, the solutions to the equation are x = 0 and x = 20.