HELP!!!!!! i need help on this math problem, its pretty hard ....?

Question

find the product of all real solutions of:

16x^2+x+4=32x^2+2x


^2=squared

Answer 1

ok, so we want to find the real numbers that x could be
first, we get everything on one side and 0 on the other
so subtract (16x^2 + x +4) from both sides
you get:
0 = 16x^2+x-4
This is a parabola, so it will have 2 solutions

it's not factorable, so you have to use the quadratic formula
if you don't know it, it's for an equation ax^2 + bx +c = 0
x = [-b +/- sqrt(b^2-4ac)]/2a

if you plug in the values of a (16) b (1) and c (-4)
you get

x= [-1 +/- sqrt (1-(4*16*-4))]/2*16

which simplifies to

x = [-1 +/- sqrt(257)] / 32

so the two real solutions are

[-1 + sqrt(257)] / 32 (approximately .4697)
and
[-1 - sqrt(257)] / 32 (approximately -.5322)

now, you want the product of these two numbers

so you multiply them, and you get

[-1 + sqrt (257)][-1 - sqrt(257)]/1024

you can factor out a -1 from each term

-1[1 - sqrt (257)] *-1[1 + sqrt(257)]/1024

the -1's multiply to equal 1

the top two factors multiply to yield a difference of squares (you can FOIL these binomals, but the middle terms will drop out)

so you get

[1-257]/1024

which simplifies to

-1/4

Answer 2

Rewrite the equation as
16x^2 + x - 4 = 0
Then divide by 16 to get
x^2 + x/16 - 1/4 = 0

Now if the (real or complex) factors of a quadratic are (x-a)(x-b), the solutions are a, b and the constant in the polynomial is (-a)(-b) = ab. [This can also be extended to higher-order polynomials.] So if there are any real solutions for this quadratic, their product is -1/4. But we know there are two real solutions because the discriminant is (1/16)^2 - 4(-1/4) > 0. [We don't have to evaluate it - it's a positive minus a negative, so must be positive.] So there are two real solutions and their product is -1/4.

Answer 3

Passing all terms to one side

16x^2 +x-4=0

Youshould know that in a 2nd degree equacion

ax^2 +bx +c=0 the sum of the roots is Sum = -b/a and the

product = c/a

so in this case product = -4/16= - 1/4

Answer 4

Time of quick Sam: = a million/ninety + a million/100 and ten = 11/990 + 9/990 = 20/990 or 2/ninety 9 Time of cruising Carla: = 2/100 or a million/50 answer: Cruising Carla received the race. Checking: Time of cruising Carla is less than than of quick Sam: = Time of quick Sam - Time of cruising Carla = 2/ninety 9 - a million/50 = 100/4,950 - ninety 9/4,950 = a million/4,950

Answer 5

for this problem you would have to use the quadratic furmula which is [-b+-the square root of (b^2-(4ac))]/2a... so the answer is( -1+- the square root of 257)/ 32

Answer 6

I know im just using this to make points but ummm i seriously do not know...im only in 6th grade so ?? err i would help you but i dont know what X is but if i did i could find the answer

Answer 7

it should be 1/4 simple algebra....hope it helps