solve: -x^4+200=102x^2?

Question

step by step help please?

Answer 1

-x^4+200=102x^2

Let x^2=t

-t^2+200=102t
0=t^2+102t-200

t=-51+ or - sqrt(2801)

x^2=-51+sqrt(2801)
x= + or - sqrt(-51+ or - sqrt(2801))

Answer 2

This is a QUARTIC equation in x, but of a particularly simple kind, since it is also QUADRATIC in the variable x^2. Thus, although as a quartic it must have 4 ROOTS, we can solve it by considering the 2 ROOTS for x^2, and subsequently find the complete set of 4 ROOTS for x from those 2 roots for x^2.

Rewrite the equation by gathering all terms on one side of the
' = ' sign :

x^4 + 102 x^2 - 200 = 0.

This is a quadratic equation in the variable x^2. It doesn't factorize. Therefore, solve it by using the usual formula,

x^2 = [- b +/- sqrt(b^2 - 4 a c)] / 2 where a x^4 + b x^2 + c = 0.

That gives:

x^2 = 1.92447449... or - 103.92447449... .

[CHECK: the SUM of these roots is - 102, which is " - b / a "; their PRODUCT is - 200, that is " c/a " --- as both of these combinations of roots should be. So far, so good!]

The second of these values for x^2 being NEGATIVE, the corresponding roots for ' x ' itself will be purely IMAGINARY. Use ' i ' for sqrt(- 1). Then the FOUR roots of the original QUARTIC equation are:

x = +/- 1.387254299... and +/- 10.19433541... i .

Live long and prosper.

Answer 3

in case you ever took precalculus or another math type which covers properties of purposes, you pointers on the thank you to ascertain the area of the function. between the crimson flags to look out for is once you divide by utilising 0. on your expression, while x = 3, the denominator is 0. to that end, the area is each and every variety beside 3. regrettably, the variety you attempt to plug in (x = 3) is the only variety that would not paintings in this function. to ascertain this universal hand, you0 can graph this function on a TI-eighty 3. in case you zoom in on the brink of the graph at x = 3, you will see that there is a sparkling spot there! this is by way of the fact, as pronounced above, there merely isn't a value of the expression at x = 3. you're able to say, properly it feels like the respond ought to be 6, finding on the graph. this concept of what the respond "ought to be" is what limits are all approximately. The values of the function on the left and supreme of x = 3 all bypass in the direction of 6 as you catch up with and closer. So we are saying the shrink as x is going to 3 is 6. So besides the reality that it's not technically the respond, 6 is your proper determination. 0 merely isn't ultimate in any sense. the very proper answer is to assert that the expression is undefined at x = 3. This project illustrates why 0/0 is termed indeterminate. in this project, 0/0 in a manner equals 6. the concept that 0/0 can equivalent something is incredibly the essence of calculus.

Answer 4

-x^4 + 200 = 102 x^2
0 = x^4 - 200 + 102x^2
x^4 + 102x^2 - 200 = 0

using quadratic formula...

x^2 = -51 +- sqrt 2801
= approx 1.924 and -103.924

since a square can't equal a negative number, we can eliminate the -103.924

x^2 = 1.924 (or -51+sqrt 2801)
take the square root of both sides...

x = 1.39 approx
or sqrt(-51 + sqrt 2801)

Answer 5

x^4 + 102x^2 - 200 = 0
x^4 + 102x^2 + 51^2 - 51^2 - 200 = 0
(x^2 + 51)^2 - 2801 = 0
(x^2 + 51 + sqrt2801)(x^2 + 51 - sqrt2801) = 0
x^2 = - 51 - sqrt 2801 impossible

x^2 = -51 + sqrt2801 => x = +/- 1.388

Answer 6

-x^4 - 102* x^2 +200 = 0

then t= x^2 and the equation becomes
-t^2 - 102 * t +200 =0

solve for t then solve for x

Answer 7

Let u = x²
u² + 102u - 200 = 0
Use the Quadratic formula to solve for u.
Substitute x² for u & solve for x.