When asked his age, michael said, "if you square
my age, then subtract 12 times my age, the result
is 85." how old is he?

Step-by-step explanation:

          Let x = Michael's age.

     Then x² = the square of his age

and x² - 12x = the square of his age – 12 times his age

and x² - 12x = 85

We must solve the quadratic for x.

1. Subtract 85 from each side.

x² - 12x - 85 = 0

2. Multiply the leading coefficient and the constant

1 × 85 = 85

3. Find two numbers that multiply to give -85 and add to give -12.

Possible pairs are 1, 85; 5, 17

Start with the numbers near the end of the list.

By trial and error, you will find that 5 and -17 work:

5 ×(-17) = -85  

and 5 -  17 = -12

4. Rewrite -12x as 5x -17x

x² + 5x – 17x - 85 =0

5. Factor by grouping the first two and the last two terms

x(x + 5) - 17(x + 5) =0

(x  + 5)(x - 17) = 0

6. Find the zeroe

Check:

OK.