SOLUTION: How do you complete the square for a quadratic function

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Question 2913: How do you complete the square for a quadratic function

Answer by creepone(1) About Me  (Show Source):
You can put this solution on YOUR website!
Completing the square is quite easy. Suppose we have a quadratic equation +f%28x%29+=+ax%5E2+%2B+bx+%2B+c+=+0. We assume that a is not equal zero, because in that case we couldn't speak of quadratic equation. Now we can write +f%28x%29+=+a%28x%5E2+%2B+%28b%2Fa%29x+%2B+%28c%2Fa%29%29+=+0+ and dividing by a we get +x%5E2+%2B+%28b%2Fa%29x+%2B+%28c%2Fa%29+=+0+. As we want to get that formula in something like +%28x%2Bm%29%5E2+=+n+ now it's our deal to ensure that +x%5E2+%2B+%28b%2Fa%29x+%2B+%28c%2Fa%29+=+%28x%2Bm%29%5E2+-+n+. This we can do simply by writing . So now we have what we wanted just by putting +m+=+b%2F%282a%29%2C+n+=+%28b%2F%282a%29%29%5E2+-+c%2Fa+. To be more concrete we can show an example of that method. +2x%5E2+%2B+4x+%2B+4+=+0+. First, we divide by 2 an we obtain +x%5E2+%2B+2x+%2B+2+=+0+. Now we can write +x%5E2+%2B+2x+%2B+2+=+x%5E2+%2B+2x+%2B+1+-+1+%2B+2+=+%28x%2B1%29%5E2+%2B+%282+-+1%29+=+0+ and so +%28x%2B1%29%5E2+=+-1+. From this equation we see that it has no real roots because the square cannot be a negative number.