2x^2/(5-x)(2-x)= 18 solve for x?

Question

What are the steps in solving this problem?
Thank You!

Answer 1

1. multiply both sides by (5-x)(2-x) to clear out the denominator. This will give you 2x^2=18(10-7x+x^2)
2. Distribute the 18 to give 2x^2=18x^2-126x+180
3. combine like terms to give 16x^2-126x+180=0
4. Either factor the equation or use the quadratic equation to solve for x.

*Be sure to check by plugging the answers back into the original equation because if x=5 or 2, it will give you a non-real number in the denominator...


Hope that helps!

Answer 2

First, I'd multiply through by (5-x)(2-x) to get rid of the denominator. (Just bear in mind, x can't be 5 or 2, since your initial equation would then have a zero denominator).

2x^2 = 18*(5-x)(2-x).
2x^2 = 18*(10 -5x -2x +x^2)
2x^2 = 180 - 126x + 18x^2
Rearranging, we get:
16x^2 - 126x + 180 = 0
8x^2 - 63x + 90 = 0

Then you just apply the quadratic formula to get the answer.

Hope that helps!

Answer 3

assume you meant:
2x^2 / { (5 - x) (2 - x) } = 18

Use FOIL
2x^2 / (10 - 5x - 2x + x^2) = 18

2x^2 / (10 - 7x + x^2) = 18

multiply 10 - 7x + x^2 for both sides
2x^2 = 180 - 126x + 18x^2

subtract 2x^2 for both sides
0 = 180 - 126x + 16x^2

factor
0 = 2(x - 6) (8x - 15)

x = 6 or 15/8

Answer 4

ideal solutions as follows:- a million:- -6,+6 2:- -6 ,+6 3:- -a million,+2 4:-2 ±?21 4 5:-3,-2/3 6:--11 ±?13 18 answer 7:- -5 ±?109 14 8:- -5 ±?7 9 9:--3 ±?29 answer 10:- -2 ±?ninety 4 10 u made a stupid mistake verify it lower back u gets it suitable

Answer 5

2x^2/10-5x-2x+x^2=18
2x^2/10-7x+x^2=18
Eliminate the denominator by multiply both sides with 10-7x+x^2
2x^2=18(x^2-7x+10)
2x^2=18x^2-126x+180
16x^2-126x+180=0
(16x-30)(x-6)=0
16x-30=0
16x=30
x=30/16
x=15/8=1/7/8
x-6=0
x=6
X=1/7/8 or 6

Answer 6

Multiply both sides by the denominator.
Subtract the right-hand side from both sides.
Expand the 18*(5-x)(2-x) product, and collect terms.
Use the quadratic formula.

You will get 15/8, 6.

Hope that helps.

Answer 7

2x^2/(5-x)(2-x)=18
2x^2=18(5-x)(2-x)
2x^2=18(10-5x+x^2-2x)
2x^2=18(10-7x+x^2)
2x^2=180-126x+18x^2
-18x^2+2x^2+126x-180=0
-16x^2+126x-180=0
a=-16
b=126
c=-180
Delta=b^2-4ac
Delta=(126)^2-4(-16)(-180)
Delta=4356
=>Square root of Delta=Square root of 4356=66
There are 2 answers for this problem 'cause the square root of Delta>0
x'=(-b-square root of Delta)/2a
x'=[-(126)-66]/2(-26)
x'=48/13

x''=(-b-square root of Delta)/2a
x''=[-(126)+66]/2(-26)
x''=15/13

The 1st answer is: 48/13
The 2nd answer is: 15/13

Answer 8

2x^2=18(10-2x-5x+x^2)
2x^2=18(10-7x+x^2)
2x^2=180-126x+18x^2
16x^2-126x+180=0 / :2
8x^2-63x+90=0
x1,2=(63+-sqrt(3969-2880))/16
x1,2=(63+-sqrt(1089))/16
x1,2=(63+-33))/16
x1=15/8 x2=6