Please, use a calculator to solve this equation to 3 signigicant digits. How did you do it?

Question

I'm having trouble figuring out this equation. It's been too long. I need to know how you solve for x on this equation. Please be specific. Thank you.


(2.32x)/(x-2) - 3.76/x = 2.32

Answer 1

Multiply by x(x-2) to get everything out of the denominators, first. Then maybe you will have a quadratic equation to solve:

(2.32x)/(x-2) - 3.76/x = 2.32
(2.32x)*x - 3.76*(x-2) = 2.32 * x * (x-2)
2.32x^2 - 3.76(x-2) = 2.32x(x-2)
2.32x^2 - 3.76x + 7.52 = 2.32x^2 - 4.64x

It turns out that the 2.32x^2 on both sides cancels, so it's just an equation of degree 1:

- 3.76x + 7.52 = - 4.64x
(4.64 - 3.76) x = -7.52
0.88x = -7.52
x = -7.52/0.88
x = -8.54545454...

To three significant digits, that's x = -8.55 (Note that "three significant digits" means three digits only, counting the 8 in the ones digit. It's not "three digits to the right of the decimal point" -- that would be "three decimal places" instead.)

Answer 2

that's good generic that the formula for fixing irreducible cubic polynomials with 3 extremely roots continuously includes cube roots of complicated numbers, or if one prefers, trigonometric purposes. as a consequence this occasion is in lots of cases stated because of the fact the "casus irreducibilis". For this distinctive polynomial the roots are two times the actual aspects of different 9th roots of solidarity. One is 2Re(w)^(a million/3) the place w is a primitive cube root of cohesion. In trigonometric type the roots of the polynomial are: 2cos(8?/9), 2cos(4?/9), 2cos(2?/9) you will, in this occasion mask the trigonometric kind with the help of increasing in a Taylor sequence approximately ?/5, even nevertheless it particularly is rarely a sensible factor to do. it ought to, for example, appear like this: (a million + ?5)/2 - (a million/2 of)?2?(5 - ?5)(?/40 5) - (a million/4) (a million + ?5)(?/40 5)^2 + a million/12?2?(5 - ?5)(?/40 5)^3 + (a million/40 8)(a million + ?5)(?/40 5)^4 - a million/240?2?(5 - ?5)(?/40 5)^5 - ... Which if i did no longer make a typo equals 2cos(2?/9) perfect to approximately 10^(-9).

Answer 3

(2.32x)/(x-2) - 3.76/x = 2.32

You want to get everything to a common denominator. The current denominators are x-2, x, and 1, respectively. x-2, x, and 1 all go into x^2-2x.

So, you get:
(2.32x)(x)/(x^2-2x) - (3.76)(x-2)/(x^2-2x)=(2.32)/(x^2-2x)

Simplify.

(2.32x^2)/(x^2-2x) - (3.76x-7.52)/(x^2-2x)=(2.32)/(x^2-2x)

Now, we can't subtract (2.32x^2) - (3.76x-7.52), but we can get rid of the parenthesis.

- (3.76x-7.52) turns into

-3.76x+7.52

So now we have

(2.32x^2-3.76x+7.52)/(x^2-2x)=(2.32)/(x^2-2x)

Then we can get rid of the denominators by multiplying both sides by x^2-2x.

So now we get:
2.32x^2-3.76x+7.52=2.32

Subtract 7.52 from both sides:

2.32x^2-3.76x= -5.20

Add 5.2 to both sides.

2.32x^2-3.76x+5.2=0

We can multiply through by 100 to get rid of the decimals.

232x^2-376x+520=0

Then you can either use quadratic formula or factor it to solve.

Hope this helps ;)

Answer 4

the answer is x = -8.545

here's the solution:

2.32x/(x-2) - 3.76/x = 2.32

multiplying both sides by 2.32, we have

x / (x-2) - 3.76/ 2.32x = 1

using the basic algebraic manipulation, we got

2.32x (x)- 3.76 (x -2) = (x -2 ) (2.32 x)

simplifying

2.32x^2-(3.76x-7.52) = 2.32x^2- 4.64x
-3.76x+7.52 = -4.64x
0.88x = -7.52
dividing both sides by .88, we have

x = - 8.545

Answer 5

2.32x / (x - 2) - 3.76 / x = 2.32
2.32x² - (3.76).(x - 2) = 2.32.(x).(x - 2)
2.32x² - 3.76x + 7.52 = 2.32x² - 4.64x
4.64x - 3.76x = - 7.52
0.88 x = - 7.52
x = - 7.52 / 0.88
x = - 8.56 ( to 2 dec. places)