Question

If x is a real number, find 49x^2+14x(19-7x)+(19-7x)^2. so so far i tried to simplfy this eqaution to 49x^2+(19-7x)(14x+19-7x)=49x^2+(19-7x)(7x+19) but idk what next ;-;

Answer 1

no, it's similar to that question you asked previously

you have to use the formula

\( a^2 + 2ab + b^2 = (a+b)^2\)

so your question is

\( 49x^2 + 14x(19-7x) + \color{orange}{(19-7x)}^2\)

do you see how you can write 49x^2 as (7x)^2

\( \color{red}{(7x)}^2 + 14x(19-7x) + \color{orange}{(19-7x)}^2\)

Answer 2

i see it but i am a bit confused on what to do on that. can you explain in a different way?

Answer 3

well your question is a bit incomplete?

is that whole equation equal to 0?

Answer 4

i guess thats all i have sadly :(

Answer 5

but otherwise basically

\( \color{red}{a}^2 + 2\color{red}{a}\color{orange}{b} + \color{orange}{b}^2 = (\color{red}{a}+\color{orange}{b})^2\)


\( \color{red}{(7x)}^2 + 14x(19-7x) + \color{orange}{(19-7x)}^2 = ??\)

and so you can just factor the equation

Answer 6

oh so (7x+19-7x)^2 and then is x (19)(19)???

Answer 7

yeah (7x+19-7x)^2 is correct

I guess they just wanted you to factor it?

Answer 8

so x is 361?

Answer 9

Yup!

because 7x - 7x = 0

and you're left with 19^2

Answer 10

I didn't realize immediately that 7x would cancel out with -7x haha

Answer 11

thx so much :)

Answer 12

you're welcome :)