Final answer:
The quadratic equation 5x² = 60 can be solved by dividing both sides by 5 to get x² = 12 and then taking the square root, yielding two solutions, x is approximately ±3.46.
Step-by-step explanation:
The task is to solve the quadratic equation algebraically. We are given the equation 5x² = 60. To solve for x, we need to isolate x on one side of the equation. First, divide both sides of the equation by 5 to simplify the equation to x² = 12. After that, we take the square root of both sides.
When taking the square root of a variable squared, remember that there are two solutions: the positive and negative roots. Therefore, we find that x is approximately ±3.46, considering approximations of square roots that aren't perfect squares.