Question
Find the number which when added to it's square gives a total of 42
Answers
GPT 3.5
To solve this problem, let's assign the number we're looking for as 'x'.
According to the problem statement, when this number is added to its square, the result is 42. Mathematically, we can express this as:
x + x^2 = 42
We can rearrange the equation into a quadratic form:
x^2 + x - 42 = 0
Now, let's factorize or solve this quadratic equation:
(x - 6)(x + 7) = 0
Setting each factor equal to zero:
x - 6 = 0 or x + 7 = 0
Solving for x in each case:
x = 6 or x = -7
Therefore, the two possible solutions are x = 6 and x = -7.
According to the problem statement, when this number is added to its square, the result is 42. Mathematically, we can express this as:
x + x^2 = 42
We can rearrange the equation into a quadratic form:
x^2 + x - 42 = 0
Now, let's factorize or solve this quadratic equation:
(x - 6)(x + 7) = 0
Setting each factor equal to zero:
x - 6 = 0 or x + 7 = 0
Solving for x in each case:
x = 6 or x = -7
Therefore, the two possible solutions are x = 6 and x = -7.