**Sheri uses the quadratic formula to find the missing base
for Don's age**

**Don had Sheri solve x ^{2}
- 5x +
6 = 0 using the quadratic formula. She
knew what the two answers were {2,3}, but Don helped her to substitute in the
formula, then get the two answers:**

**Don
had Sheri list what a, b and c are in** **x ^{2}
- 5x + 6 = 0; a = 1, b= **

^{- }5 and c=6. a=1
was not obvious; they talked about what times x^{2} = x^{2}
? 1. Don substituted these values of a, b, and c into the formula:

**They
got The ' means
"plus or minus" and this gives the two answers as shown above. Sheri
then solved another quadratic equation (for which she knew the answers), using
the using the formula, then solved x ^{2}
+ x + 4 = 71 or x^{2} + x - 67 = 0 to
find the base for Don's age:**

**These two exact answers are approximately ****7.700609733...
and -8.700609733. Sheri got the first answer, but didn't
have time to get the second one. Notice that in using the calculator to do find
the base earlier, Sheri got 7.7, which was very close to the answer using the
quadratic equation. So Don's "age" of 114 is in base 7.7 to get his
real age of 71!**

**There are many good questions that Don thinks
of now..what do you think?**

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