Final answer:
To solve the equation 6x^2 + 1 = 13, subtract 1 from both sides, divide by 6, then take the square root of both sides, resulting in solutions x = √2 and x = -√2.
Step-by-step explanation:
To solve the equation 6x^2 + 1 = 13, follow these steps:
Subtract 1 from both sides of the equation to isolate the quadratic term, which gives us 6x^2 = 12.
Divide both sides by 6 to solve for x^2, resulting in x^2 = 2.
Find the square root of both sides to solve for x, which gives us x = ±√2. The ± symbol indicates that there are two solutions: x = √2 and x = -√2.
Check the answer to see if it is reasonable. In this case, substituting x = √2 or x = -√2 back into the original equation should yield a true statement.
Therefore, the solutions to the equation are x = √2 and x = -√2.