Help With Quadratic Equations

[TiaharaJBennett]

Hello!

Okay, so I really need some help with quadratic equations.

Right now I'm working on 2x^2+3x-1=0. I've gotten as far as this: 3 plus or minus the square root of 17. When I try to find the square root of 17, it's a decimal. That part threw me off. Can anyone explain how I solve this? Thanks!

 

[mmm4444bot]

I'm working on 2x^2 + 3x - 1 = 0

I've gotten … 3 plus or minus the square root of 17.

Those are not the correct solutions. I think you have sign issues and a missing denominator.

Please show your work.

When I try to find the square root of 17, it's a decimal. That part threw me off.

Well, does this exercise's instruction require you to report decimal approximations? What exactly is the meaning of "That part threw me off"? (I hope that you are not on the floor.)

Please also check our FORUM GUIDELINES for information about how to ask for help. Cheers :cool:

 

[TiaharaJBennett]

Those are not the correct solutions. I think you have sign issues and a missing denominator.

Please show work.

Okay, here is my work:

x=-(3)±√(3)²-4(2)(-1)/ 2(2)

x= 3±√9+8/4= 3±√17/4

That's how far I got. No, it does not say anything about decimal approximations.

 

[mmm4444bot]

x=-(3)±√(3)²-4(2)(-1)/ 2(2)

x= 3±√9+8= 3±√17
4 4

Okay -- I see that the correct denominator (which is missing from your original post) has been located. That's good.

What's up with the -(3) turning into 3? :cool: Perhaps, it's another typo.

it does not say anything about decimal approximations

Then forget about approximating the number sqrt(17) in your solutions.

Simply report the (exact) answer, as is.

---

Here are some comments about texting mathematical expressions. Do not try to "draw" fractions; use grouping symbols, instead. In particular, be sure to place grouping symbols around any numerator or denominator that consists of more than one term or symbol AND any similar expression inside a radical sign (as shown in your edited copy below). Oh, and try to avoid writing equations using more than one equals sign; kindly write each equality on its own line.

x = (-3 ± √[3² - 4(2)(-1)])/[2(2)]

x= (-3 ± √[9+8])/4

x = (-3 ± √17)/4

Otherwise, good job.

Cheers ~ Mark

 

[TiaharaJBennett]

Okay -- I see that the correct denominator (which is missing from your original post) has been located. That's good.

What's up with the -(3) turning into 3? :cool: Perhaps, it's another typo.

Yeah. I tried searching online to figure out how to solve. I was just following what I saw, but I wasn't sure if it was right.

Then forget about approximating the number sqrt(17) in your solutions.

Simply report the (exact) answer, as is.

Okay, so I just go ahead and use it? The decimal is 4.123.

 

[mmm4444bot]

I was just following what I saw, but I wasn't sure if it was right.

If you saw some positive number turn into its opposite without a valid operation to justify that change, then what you saw is incorrect.

Okay, so I just go ahead and use the decimal?

No. By mentioning the "exact" answer, I intended for you to realize that the expression

\(\displaystyle \frac{-3 \pm 4.123}{4}\)

is an approximation AND that the expression

\(\displaystyle \frac{-3 \pm \sqrt{17}}{4}\)

is exact.

Do not use decimal approximations for anything unless you are specifically instructed to report a decimal approximation for the final result. Report the exact version, instead.

 

[TiaharaJBennett]

No. By mentioning the "exact" answer, I intended for you to realize that the expression

\(\displaystyle \frac{-3 \pm 4.123}{4}\)

is an approximation AND that the expression

\(\displaystyle \frac{-3 \pm \sqrt{17}}{4}\)

is exact.

Do not use decimal approximations for anything unless you are specifically instructed to report a decimal approximation for the final result. Report the exact version, instead.

Oh, okay. I understand now. Thanks for helping me, Mark!
But how do I continue to get the final result? (Sorry, math just isn't my best subject :|
)

 

[mmm4444bot]

how do I continue to get the final result

Both of the expressions at the end of my previous post are valid solutions to the given equation.

However, I'm telling you to use the exact version.

In other words, here are the two "final" solutions:

x = (-3 + √17)/4

x = (-3 - √17)/4


Not every answer in algebra has to be reduced to a single number. Are you taking a course on-line?

~ Mark

PS: I regret that I have no formal training in education.

 

[TiaharaJBennett]

Both of the expressions at the end of my previous post are valid solutions to the given equation.

However, I'm telling you to use the exact version.

In other words, here are the two "final" solutions:

x = (-3 + √17)/4

x = (-3 - √17)/4


Not every answer in algebra has to be reduced to a single number. Are you taking a course on-line?

~ Mark

PS: I regret that I have no formal training in education.

Thank you SO much! So, I just leave I could just leave it as x = (-3 + √17)/4?

No, I am not taking a course online. I have two other equations that are similar. Do I do the same for those? Their square roots are decimals too!

You DON'T have formal training? Then how are you so good at this?

 

[srmichael]

Thank you SO much! So, I just leave I could just leave it as x = (-3 + √17)/4? AND x = (-3 - √17)/4

No, I am not taking a course online. I have two other equations that are similar. Do I do the same for those? Their square roots are decimals too!

You DON'T have formal training? Then how are you so good at this?

.

 

[TiaharaJBennett]

Thank you!

 

[mmm4444bot]

Do I do the same for those? Their square roots are decimals too!

Do not use decimal approximations for anything unless you are specifically instructed to report a decimal approximation …

PS: Anytime you see a \(\displaystyle \pm\) symbol, it denotes two different expressions (one with addition and one with subtraction). That symbol is used to abbreviate the writing of two separate expressions into a single "combo pack" statement. If you abbreviate your answer this way, don't forget to use the \(\displaystyle \pm\) symbol.

 

[TiaharaJBennett]

PS: Anytime you see a \(\displaystyle \pm\) symbol, it denotes two different expressions (one with addition and one with subtraction). That symbol is used to abbreviate the writing of two separate expressions into a single "combo pack" statement. If you abbreviate your answer this way, don't forget to use the \(\displaystyle \pm\) symbol.

Got it! Thanks again!