Final answer:
To solve (x+20)²/3=3x, raise both sides to the power of three to eliminate the fractional exponent, form the quadratic equation, and then use the quadratic formula to find the possible values for 'x'.
Step-by-step explanation:
To solve the equation (x+20)²/3=3x, we first recognize that the equation has a quadratic form where one side is a perfect square. To simplify the equation, we can raise both sides to the power of three to eliminate the fractional exponent. The given equation changes to (x+20)² = (3x)³, which transforms into a quadratic equation when expanded. The steps to find the solution to a quadratic equation include:
- Expanding both sides of the equation if necessary
- Rearranging terms to form ax² + bx + c = 0, where 'a', 'b', and 'c' represent constants
- Using the quadratic formula to solve for 'x'
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), where 'a' is the coefficient of the x² term, 'b' is the coefficient of the x term, and 'c' is the constant term.
Applying the quadratic formula to our equation after organizing it into standard form will yield the possible values for 'x', and we can determine which of the provided options (A, B, C, or D) is a valid solution.