Question

Solve with the square root method

Answer 1

`x= 7 + 2√(15) \\x= 7 - 2√(15)`

Explanation:

To solve the equation (x - 7)^(2) = 60, we can start by taking the square root of both sides:

`√((x-7)^2) = √(60)`

Simplifying, we get:

x - 7 = ±
`√(60)`

Now we can add 7 to both sides to isolate x:

x = 7 ±
`√(60)`

To simplify further, we can factor 60 into its prime factors: 60 = 2^(2) * 3 * 5.

Then, we can simplify the square root of 60:

`√(60) = √(2^2*3*5) = 2√(15)`

So the final solutions are:

`x= 7 + 2√(15) \\x= 7 - 2√(15)`