Question 130837
Melinda is x years old now.
Dad is x + 30 years old now.
Eight years ago, Dad was x + 30 - 8 = x + 22 years old, and Melinda was x - 8 years old.  Melinda's age squared 8 years ago would then be {{{x^2-16x+64}}}.


{{{x^2-16x+64=x+22}}}


{{{x^2-17x+42=0}}}


{{{-14*-3=42}}} and {{{-14-3=-17}}}, so:


{{{(x-3)(x-14)=0}}}.  So, Melinda is either 3 years old, or she is 14 years old.  But the answer 3 is absurd, because that means her age 8 years ago was -5.  So we can exclude that answer as an extraneous root caused by squaring the variable when we set up the problem in the first place.  The correct answer is Melinda is 14.


Check:
14 + 30 = 44

14 - 8 = 6, 6 X 6 = 36, and 44 - 8 = 36, answer checks.