Final answer:
The solution to the equation 5x² = 60 is found by dividing both sides by 5, yielding x² = 12, then taking the square root to obtain x = ±√(12), which simplifies to x = ±(2√3). The correct answer is not listed in the provided choices.
Step-by-step explanation:
The student has asked to solve the equation 5x² = 60 algebraically. To find the solution, we first divide both sides of the equation by 5 to isolate x²:
5x² = 60
x² = 60 / 5
x² = 12
Now we need to take the square root of each side of the equation to find x. As we are solving an equation, it is important to consider both the positive and negative roots of x²:
x = ±√(12)
Therefore, the solution to the equation is x = ±√(12), which simplifies to x = ±√(4 ∙ 3) or x = ±(2√3).
To answer the student's question, the option that matches this solution is not provided in the choices (a. x² + 3.46, b. x² - 3.46, c. x = 12, d. x = 12), as none of these represent the algebraic solution of ±(2√3).