Completing the square of: 2x^2 - 12x + 11

[Math_Junkie]

Completing the square of: 2x^2 - 12x + 11

I don't know how to handle this?

 

[mmm4444bot]

I don't know how to handle [completing the square] …

Hi:

Before we complete the square, we need the leading coefficient to be 1.

So, start by factoring out 2.

Are you trying to tell us that you have not yet studied how to complete the square?

I'm not sure why you're stuck. :?

Cheers,

~ Mark

 

[soroban]

Hello, Math_Junkie!

Complete the square: .\(\displaystyle 2x^2 - 12x + 11\)

\(\displaystyle \text{Factor out the 2: }\:2\bigg(x^2 - 6x + \frac{11}{2}\bigg)\)

\(\displaystyle \text{Inside the parentheses, add 9 and subtract 9: }\;2\bigg(x^2 - 6x + 9 - 9 + \frac{11}{2}\bigg)\)

\(\displaystyle \text{We have: }\;2\bigg(x^2 - 6x + 9 - \frac{7}{2}\bigg) \;=\;2\bigg([x-3]^2 -\frac{7}{2}\bigg)\)

\(\displaystyle \text{Multiply by 2: }\;2(x-3)^2 - 7\)

 

[Math_Junkie]

Thank you very much! It was factoring out the 2 that confused me a bit.

Thanks again to both of you.