Math 2 More Options: Make a Folding Card

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• Foil That!
• Now, remember that (a-6)^2 is the same as (a-6)(a-26). This means you have to use FOIL to create a standard form equation.
• After using FOIL, I got a=a^2-12a+36
• Set it to 0
• Subtract a from both sides?
• Now, you'll need to set it to 0.
• Correct!
• Find the X's
• I'm going to factor it and then set it to 0.
• Good thinking!
• Now, solve for your x's. You may use whatever method you want.
• Work  √a=a-6  ( √a)^2=(a-6)^2  a=(a-6)(a-6) -> a=a^2-12a+36
• Time to Substitute
• Let's substitute the new values in for a.
• Work  √a=a-6  ( √a)^2=(a-6)^2  a=(a-6)(a-6) -> a=a^2-12a+36 a-a=a^2-12a+36-a -> 0=a^2-13a+36
• Wow That's Interesting
• What is an extraneous solution?
• Work  √a=a-6  ( √a)^2=(a-6)^2  a=(a-6)(a-6) -> a=a^2-12a+36 a-a=a^2-12a+36-a -> 0=a^2-13a+36 -> 0=(a-9)(a-4)   a-9+9=0+9-> a=9  a-4+4=0+4 -> a=4
• The End
• a=9 is the actual solution which means it worksand a=4 is the extraneous solution.
•  √9=9-6 -> 3=3 ✓  √4=4-6 -> 2=-2 ❌
• √9=9-6 -> 3=3 ✓  √4=4-6 -> 2=-2 ❌
•  a-9+9=0+9-> a=9  a-4+4=0+4 -> a=4         a=9 a=4  √a=a-6   √9=9-6 -> 3=3 ✓  √4=4-6 -> 2=-2 ❌ Not an actual solution since it does't sastify the original equation.
• I plugged in both values but a=4 does not work. Why is that?
• This the part where I got confused.
• Don't worry Mike, that's what we mathmeticians like to call an extraneous solution.
• You got this.
• Professor Smith explains what an extraneous solution is and they depart.
• Thanks Professor,  I was very confused.
• No need to thank me. Anytime Mike.
• It is just a solution that does not work when substituted into your original equation. It happens but you would want to distinguish it from your actual solution which in this case is a=9 since it works.
• Mike explains the problem that was once haunting him and he explained it to his math class. He received extra credit from his math teacher and applause from his classmates.
• An extraneous solution is a solution that does not satisfy the original equation. It needs to be distinguished from the actual solution.
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