Final answer:
To solve the equation 3x² = 375, divide by 3 to get x² = 125 and then take the square root, resulting in x = ±√125, which simplifies to x = ± 5√5.
Step-by-step explanation:
We need to solve the equation 3x² = 375 algebraically. The first step is to simplify the equation by dividing both sides by 3, which will give us the new equation x² = 125. Now, we can take the square root of both sides to solve for x. Remember that taking the square root of a number yields both a positive and a negative solution, so we get x = ±√125.
Now, √125 can be simplified further since 125 is a perfect cube of 5. So, we have x = ± 5√5. This is our final solution for the given quadratic equation.