Thanks Reiny, but I'm still lost. I understand how you multipled by 10X on the right to get 17x, but you went too fast on the left, and I have no idea how you got 10x^2-20 from the starting left side. Can you show each step?
Thanks,
Carol
x - 2(1/x) = 17/10
multiply each term by 10x
10x^2 - 20 = 17x
10x^2 - 17x - 20 = 0
(5x + 4)(2x - 5) = 0
so x = -4/5 or x = 5/2
check:
reciprocal of 5/2 is 2/5
twice the reciprocal is 4/5
evaluate 5/2 - 4/5
= (25-8)/10 = 17/10
x * 10x = 10x^2
2/x * 10x = 20 (The x's cancel each other out.)
Thus 10x(x -2/x) = !0x^2 - 20
I hope this helps a little more. Thanks for asking.
Sure Carol, I apologize for going too fast. Let me break down the steps for you:
Starting equation: x - 2(1/x) = 17/10
1. Multiply each term by 10x to eliminate the fraction:
(10x)(x) - (10x)(2)(1/x) = (10x)(17/10)
Simplify:
10x^2 - 20 = 17x
2. Rearrange the equation to set it equal to zero:
10x^2 - 17x - 20 = 0
3. Factor the quadratic equation:
To factor 10x^2 - 17x - 20, you need to find two binomials that multiply to give you 10x^2 - 17x - 20 and add up to -17x. The factors are (5x + 4) and (2x - 5):
(5x + 4)(2x - 5) = 0
4. Set each factor equal to zero and solve for x:
5x + 4 = 0 -> x = -4/5
2x - 5 = 0 -> x = 5/2
So x can be either -4/5 or 5/2.
To check the solution, plug each value back into the original equation:
- For x = -4/5:
-4/5 - 2(1/(-4/5)) = 17/10
Simplify:
-4/5 + 10/4 = 17/10
(Multiply fractions and find a common denominator)
(-16 + 50)/20 = 17/10
34/20 = 17/10
Simplify further, and you'll find that both sides are equal.
- For x = 5/2:
5/2 - 2(1/(5/2)) = 17/10
Simplify:
5/2 - 2/(5/2) = 17/10
5/2 - 4/5 = 17/10
Again, finding a common denominator and simplifying will yield the same equation on both sides.
I hope this explanation helps you understand the steps involved! Let me know if you have any further questions.