Question

I need some help with this? It's soo freaking hard! My own math teacher can't even explain this to me.

Use the technique of completing the square to transform the quadratic equation into the form (x + c)2 = a.

10x2 + 80x + 220 = 0

Answer 1

expand that (x+c)^2 and compare parts

Answer 2

that's still so confusing. times each side or something?

Answer 3

(x+c)^2 expands out ... use foil if need be .. to x^2 + 2c x + c^2

Answer 4

subtract that a and compare what we got:

x^2 + 2c x + c^2 - a = 0

has to equal

10x^2 + 80x + 220 = 0 , factor out the 10 to see them on common grounds


x^2 + 2c x + c^2 - a = x^2 + 8x + 22

as such, 2c = 8, and c^2-a = 22

Answer 5

lol i still don't get it. so would be maybe be this? because this is what im getting. (x + 4)2 = -22

Answer 6

almost, c = 4 is good, but a = -22+4 :)

Answer 7

in order for 2 polynomials to be identical to each other, they have to have the same coefficients for like terms.

Answer 8

we have 10x^2 + 80x +22 = 0

and that has to match up to the expanded form of (x+c)^2 - a = 0

Answer 9

okay i think i get it now, thank you!

Answer 10

there might be someting more about that 10 that had to be factored out ... since this is just a rough recollection :) but thats the basics

Answer 11

good luck

Answer 12

Start off by grouping the facors

\[\large (10x^2 + 80x \space \space \space \space \space \space \space \space ) +220\]

Factor out a 10 to simplify...

\[\large 10(x^2 + 8x \space \space \space \space \space \space \space \space ) +220\]

Take half the coefficient of the 'x' and then square it...so

8/2 = 4...then 4^2 = 16....Put that into the parenthesis where I put the space...Now you would multiply 15 by 10 since that is our outside factor....so 160 now subtract that from the 220

\[\large 10(x^2 + 8x + 16) = 220 -160\]

Factor that parenthesis... and simplify the 220 - 160...

What do you get?