If eleven is add to the square of a number, the result is sixty. Find all such numbers.

60 - 11 = 49

What is the square root of 49?

To find all the numbers that satisfy the given condition, we need to set up an equation and solve for the variable.

Let's assume the number we are looking for is "x."

According to the problem statement, if we add eleven to the square of the number (x^2), the result is sixty:

x^2 + 11 = 60

To solve this equation, we can start by bringing the constant term (11) to the other side by subtracting it from both sides:

x^2 = 60 - 11
x^2 = 49

Now, take the square root of both sides to isolate the variable:

√(x^2) = √49
x = ±√49

Since the square root of 49 has two solutions, positive and negative, we have two possible values for x:

x = 7 (positive square root)
x = -7 (negative square root)

Therefore, the two numbers that, when added to eleven squared, give sixty are 7 and -7.