Answer is in the question
If the value of a 2 + 6 a − 6 is a , then find the minimum value of a .
The answer is -6.
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3 solutions
Maybe completing the square is the easiest for me to solve quadratics .
I'd understand, if you did 2 a + 6 = a , but why can you say a 2 + 6 a − 6 = a ?
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Because a is the solution to the problem and the (minimum) value of a 2 + 6 a − 6 is also the solution to the question, thus a 2 + 6 a − 6 = a .
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Where did the epxression a 2 − 6 a + 6 come from?
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@Patrick Engelmann – It's actually a 2 + 6 a − 6 = a .
question was like level 0
The first line in your solution is different from the question.
a 2 + 6 a − 6 = a
a 2 + 5 a − 6 = 0
( a + 6 ) ( a − 1 ) = 0
a + 6 = 0 , or x − 1 = 0
∴ x = − 6 , or x = 1
So, the minimum value of a is equal to − 6 .
Solved as a quadratic equation, a 2 + 5 a − 6 = 0 , the two answers are -6,1, and -6<1 2 × 1 − 5 + − 2 5 − 4 × 1 × − 6 = 1 , − 6
Why did you use a quadratic formula?
I solved it by factoring. (Of course, I wanted to complete square, but I couldn't because I could factor it in the range of natural numbers.)
Note that the problem says that a is the minimum value of the given expression. Thus, we must have
a 2 + 6 a − 6 a 2 + 5 a − 6 ( a + 6 ) ( a − 1 ) a = a = 0 = 0 = − 6 , 1 .
The smallest value of a is − 6 .
UPDATE: I have changed the wording of the problem slightly in hopes that it will be clearer.