Question

. Anna was thinking of a number. She told Bill that if he squared her number followed by subtracting 11 times her, and adding 4, then he would get -26. What number(s) could Anna be thinking of?

Answer 1

Anna's number could be 5 and it could be 6.

Explanation:

Let Anna's number be represented by x.

If Bill squared her number followed by subtracting 11 times her number, and adding 4, then he would get -26.

This implies that:

`x^2 - 11x + 4 = -26`

This is a quadratic equation and we can solve for x by factorization.

`x^2 - 11x + 4 = -26\\\\=> x^2 - 11x + 4 + 26 = 0\\\\x^2 - 11x + 30 = 0\\\\x^2 -6x-5x + 30 = 0\\\\x(x - 6) - 5(x - 6) = 0\\\\(x - 5) (x - 6) = 0\\\\`

=> x = 5 and x = 6

Anna's number could be 5 and it could be 6.