the square of an interger is 30 more than the integer. Find the integer.
To find the integer, we will set up an equation based on the given information.
Let's assume the integer is represented by 'x'.
According to the given information, "the square of an integer is 30 more than the integer," we can write this as an equation:
x^2 = x + 30
To solve this equation, we will set it equal to zero by subtracting x and 30 from both sides:
x^2 - x - 30 = 0
Now we have a quadratic equation. To solve it, we can either factor it or use the quadratic formula. In this case, let's factor it:
(x - 6)(x + 5) = 0
Setting each factor equal to zero, we get two possible solutions:
x - 6 = 0 --> x = 6
x + 5 = 0 --> x = -5
So, the two possible integers are 6 and -5.