Question

What are the roots of the quadratic equation xÆ – 2x + 4 = 8x – 21?

Answer 1

do you know how to factor a quadratic?

Answer 2

No

Answer 3

ok... so.. .what instructions are you meant to use to get the factors?

Answer 4

im sorry i dont understand ..

Answer 5

well.. you're expected to find the roots, or zeros

what instructions are you meant to use to find the roots ?

there are several ways... but dunno what the exercise is covering

Answer 6

I mean i honestly dont know. Im taking an online math class and its not really teaching me anything.
It just gives me problems like these and thats it .

Answer 7

hmmm well... sounds like they're not help then

you're meant to have covered that section before doing the exercises
otherwise..... I mean.. .what if decide to give you an exercise on say physics in initial velocity, if you dunno what that is.or haven't covered it.. the exercise wouldn't apply

Answer 8

Yea there really not. And its awful because i need this class to graduate. Its awful and its hard.
Thats why im on this website to get help

Answer 9

well.... do you know how to do linear simplification? like say, solving for a variable

Answer 10

yes

Answer 11

ok ... then let's see yours \(\bf x^2 - 2x + 4 = 8x - 21\) if you moved everything to the left-hand-side.... what would you be left with?

Answer 12

bearing in mind that the "x" and constant terms, simplify themselves

Answer 13

x^2-2x-8x+4-21=0 .. ?

Answer 14

Is there anyway you can help me with my other assignments ?

Answer 15

well
\(\large {
x^2 - 2x + 4 = 8x - 21\implies x^2-2x+4-8x+21=0
\\ \quad \\
x^2-10x+25=0\qquad notice\implies
\begin{array}{cccllll}
x^2&-10x&+25&=0\\
&\uparrow &\uparrow \\
&-5-5&-5\cdot -5
\end{array}
}\)

notice that, the middle term can come from ADDING 2 factors, of the last term "25"
and that the same factors can be used to produce the last term, or "25"