### Instruction: The sum of a positive number and its square is 156. What is the number?### Response: To solve this problem, I need to find a positive number x that satisfies the equation x + x^2 = 156.
I can try to rearrange this equation and make it a quadratic equation in standard form.
Subtracting 156 from both sides, I get x^2 + x - 156 = 0.
Now I can try to factor this equation and see if there are any integer solutions.
I look for two numbers that multiply to -156 and add to 1.
After some trial and error, I find that 13 and -12 are such numbers.
So I can write x^2 + x - 156 = (x + 13)(x - 12).
Setting each factor equal to zero, I get x = -13 or x = 12.
However, I only want the positive solution, so I can ignore x = -13 and focus on x = 12.
To check my answer, I can plug it back into the original equation and see if it works.
12 + 12^2 = 12 + 144 = 156, which is true.
Therefore, the positive number that satisfies the given condition is 12.