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Part 1

Part 2

This is from completing the square practice on Khan Academy. Why do we multiply the 2 on the right side? Why not just subtract 121/16.

Theo Bendit
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artdensity
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    Your question is unclear to me. We have $h(x) = 2x^2+11x+15$ which can be expressed as $2(x^2 + \frac{11}{2}x)+15$. Why would you need to subtract $\frac{121}{16}$ in this step? – Toby Mak Sep 22 '19 at 01:21
  • Could you highlight which step you're referring to? I'm also struggling to understand what you're asking. – Theo Bendit Sep 22 '19 at 01:27
  • It seems like he’s asking why they subtract $2 \frac{121}{16}$ instead of subtracting $\frac{121}{16}$. If so, it’s because you added $\frac{121}{16}$ INSIDE the parentheses, and everything inside the parentheses is being multiplied by 2, so you really added $2 \frac{121}{16}$, and therefore have to subtract the same thing. – Joe Sep 22 '19 at 01:31
  • Ah! let me rephrase. Why are we doing -2 121/16 instead of - 121/16. I don't see why you would need to multiply 2 to the other side. – artdensity Sep 22 '19 at 01:35
  • @Joe Ah! I see! Thank you! It's still the same process of completing the square. – artdensity Sep 22 '19 at 01:41
  • Yes, exactly the same. – Joe Sep 22 '19 at 01:45
  • Wait, I have another question. Why is your middle coefficient /2 is always your missing number in (x + _ ) ^2? Like in this example, 11/2 / 2 = 11/4. I suppose I could refer to this missing number as "d", according to the completing the square formula. – artdensity Sep 22 '19 at 01:59

1 Answers1

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Everything inside the parentheses is multiplied by 2, therefore, when bringing something outside the parentheses, it must be multiplied by 2 as well.

Henri
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