Question

x^2+7x-2=0 what are the solutions and what would be the x intercepts?

Answer 1

\[x^2 + 7x = 2\] ....from there, complete the square

Answer 2

would it be \[\sqrt{2},-\sqrt{2}\]

Answer 3

solutions and x-intercepts are the same thing...
try to follow my steps from the last problem.
take half of 7, square it, then add it to both sides ...

Answer 4

but i add the o into the problem to get the intercepts right

Answer 5

??

Answer 6

\[3.5^{2}\]

Answer 7

good

Answer 8

\[7x+3.5^{2}=2+3.5^{2}\]

Answer 9

good, dont leave off the x^2 though
Now factor left side

Answer 10

ok id need to add x^2 first so it would be

Answer 11

\[x ^{2}+7x+3.5\]

Answer 12

yes then it factors to
\[(x+3.5)^{2}\]

Answer 13

then i do the right side

Answer 14

would that be 14.25

Answer 15

If you start with \[x^{2} + bx = c\]
you will end up with
\[(x + b/2)^{2} = c + (b/2)^{2}\]

Answer 16

yes 14.25, good

Answer 17

now that is one solution or no

Answer 18

not yet, we have to get rid of the square
how do we do that?

Answer 19

do i now have to combine

Answer 20

you should have
\[(x+3.5)^{2} = 14.25\]
how do i get rid of the square

Answer 21

square root of both sides then subtract?

Answer 22

perfect

Answer 23

i can see how you want me to do it but im getting confused on how to accomplish it im sorry i must seem really stupid

Answer 24

perfect

Answer 25

whats confusing you? you told me how to do it...square root both sides then subtract
then you will have x alone and you are done

Answer 26

im looking at your example and trying to figure out if it should be in a fraction

Answer 27

perfect

Answer 28

sqrt(14.25) = +-3.775
x + 3.5 = +-3.775

Answer 29

perfect

Answer 30

oh i see, yes i used fractions all the way through and i came out nice
but many times you have to use your calculator to find the square roots

Answer 31

perfect

Answer 32

so no you can write things as fraction or decimal, whatever you like
\[x = \pm3.775 - 3.5\]

Answer 33

so in the end im looking for the answer as a radical

Answer 34

Fraction form is more exact

Answer 35

the first part of my problem is asking for the solutions as exact anser using radicals rationalizing all denominators as nessecary express all complex tems in terms of i and using commas to separate answers as needed, then part two is to find the x intercepts it is showing it as a graphing problem

Answer 36

ok if you need an exact answer or in radical form
then try to use fractions all the way through
ie. instead of 3.5 use 7/2
3.5^2 = 49/4

our problem would be rewritten as:
(x+7/2)^2 = 2 + 49/4 = 57/4
x + 7/2 = +-sqrt(57)/2
x = (+-sqrt(57) - 7)/2

Answer 37

remember the solution is the x-intercepts

Answer 38

in previous ones i also had 0 in each is that still the case for this problem?