Question

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?​

Answer 1

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

x=-5 or x=17

Discard the negative value

x=17 is considered.

Michael is 17yrs old

Answer 2

• 
  `\boxed{\textbf{He is 17 years old}}`

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

`(x + 5)(x - 17) = 0\\\\\begin{array}{rlrl}x + 5 & = 0 &  x - 17 & =0\\x & = -5 & x & = 17\\\end{array}\\\text{Michael can't have a negative age, so } \boxed{\textbf{he is 17 years old.}}`

Check:

`\begin{array}{rcl}(-17)^(2) + 12(-17) & = & 85\\289 - 204 & = & 85\\85 & = & 85\\\end{array}`

OK.