find the value of k in the following algebraic expression

[eddy2017]

Hi, dear tutors,
I find to find the value of k in this expression.
$$6^2 + kx-5=(2x-1) (3x+5)$$
my question is,
Do I need to find the value of x first?.
thanks,
eddy

 

[BigBeachBanana]

Are you certain you copied the question correctly? The difficulty of the question is more challenging than the typical questions that you normally post.
See graphs here:https://www.desmos.com/calculator/8aetn7a3ob

 

[eddy2017]

Are you certain you copied the question correctly? The difficulty of the question is more challenging than the typical questions that you normally post.
See graphs here:https://www.desmos.com/calculator/8aetn7a3ob

So, there's no solution like that. Are you implying that it is faulty?. Just saying. I was thinking I can FOIL the right side and solve for x to clear the k first, but after getting the value of x, what am I supposed to do. I can solve for x. I know how to do it, but then I will need your help to go to the next step.

 

[lev888]

Hi, dear tutors,
I find to find the value of k in this expression.
$$6^2 + kx-5=(2x-1) (3x+5)$$
my question is,
Do I need to find the value of x first?.
thanks,
eddy

Please double check, I think you didn't copy it correctly. There should be x², not 6².

 

[eddy2017]

Please double check, I think you didn't copy it correctly. There should be x², not 6².

Oh, sorry. Yes, lev is right.
$$x^2$$

 

[BigBeachBanana]

Oh, sorry. Yes, lev is right.
$$x^2$$

$$x^2+kx-5=(2x-1)(3x+5)$$There are many solutions for k that satisfy the equation.
See new graph: https://www.desmos.com/calculator/dkk03wah0m

 

[eddy2017]

$$x^2+kx-5=(2x-1)(3x+5)$$There are many solutions for k that satisfy the equation.
See new graph: https://www.desmos.com/calculator/dkk03wah0m

So, I'll take that to mean it is not a doable thing. Okay, thanks bbb

 

[BigBeachBanana]

So, I'll take that to mean it is not a doable thing. Okay, thanks bbb

It's doable, but k isn't just a singular value (without any constraint on x). What's the context of this problem?

 

[eddy2017]

It's doable, but k isn't just a singular value (without any constraint on x). What's the context of this problem?

Just that. they ask to find the value ok in that expression. Nothing else.

 

[BigBeachBanana]

Just that. they ask to find the value ok in that expression. Nothing else.

Please check or post the original problem. Is it possible the question is $$\red{6x^2}+kx-5=(2x-1)(3x+5)$$

 

[eddy2017]

Please check or post the original problem. Is it possible the question is $$\red{6x^2}+kx-5=(2x-1)(3x+5)$$

Yes, Bbb, very possible, there was a smudge at the beginning of the page. But confirming it with a friend, yes, it is that at the beginning, hence my initial 6.

 

[BigBeachBanana]

Yes, Bbb, very possible, there was a smudge at the beginning of the page. But confirming it with a friend, yes, it is that at the beginning, hence my initial 6.

If so, the question is solvable for a singular value of k. Show your work of FOIL for the RHS.

 

[eddy2017]

Foiling the right-hand side.
$$(2x-1) (3x+5)$$$$expanding$$$$(2x* 3x) + (2x* 5) + (-1 * 3x) + (-1 * 5)$$ 6x^2 + 10x -3x -5 $$$$6x^2 + 7x -5$$now,$$ 6x^2 + kx -5 = 6x^2 + 7x - 5$$

This is the foiling of the right-hand side

 

[BigBeachBanana]

Foiling the right-hand side.
$$(2x-1) (3x+5)$$$$expanding$$$$(2x* 3x) + (2x* 5) + (-1 * 3x) + (-1 * 5)$$ 6x^2 + 10x -3x -5 $$$$6x^2 + 7x -5$$now,$$ 6x^2 + kx -5 = 6x^2 + 7x - 5$$

This is the foiling of the right-hand side

$$6x^2 + kx -5 = 6x^2 + 7x - 5$$Now, solve for k.

 

[eddy2017]

Let's solve for k.

$$6x^2+kx−5=6x^2+7x−5$$
Addin’ -6x^2 to both sides.

$$kx+6x^2−5+−6x^2= 6x^2+7x−5+−6x^2$$
$$kx−5=7x−5$$
Addin’ 5 to both sides.

$$kx−5+5=7x−5+5$$
$$kx=7x$$
Dividin’ both sides by x.

$$kx / x = 7x/x$$
$$k=7[/I]$$

 

[eddy2017]

$$k=7$$

 

[eddy2017]

thank you,BBB.