Use the quadratic formula to solve each equation

[wdstone]

Good afternoon. I am studying for an exam and I can't quite figure out how to get the full answer to this problem, I found half but cannot figure out what to do from here. I have the answers to the problem provided from the study guide, so I know half of my answer is correct.

3x² +16x = -5

move 5 to the other side
3x² + 16x +5 = 0

plug into the quadratic formula.

-16 +- √(-16)² -4(3)(5) / 2(3) work out under the square

-16 +- √196 / 6 - sqaure and add 16

+-30/6

+-5 so now I get to this.

The answer set is {-5, -1/3} How do I get to the -1/3 answer now that I have the -5?

 

[Mrspi]

Good afternoon. I am studying for an exam and I can't quite figure out how to get the full answer to this problem, I found half but cannot figure out what to do from here. I have the answers to the problem provided from the study guide, so I know half of my answer is correct.

3x² +16x = -5

move 5 to the other side
3x² + 16x +5 = 0

plug into the quadratic formula.

-16 +- √(-16)² -4(3)(5) / 2(3) work out under the square

-16 +- √196 / 6 - sqaure and add 16

+-30/6

+-5 so now I get to this.

The answer set is {-5, -1/3} How do I get to the -1/3 answer now that I have the -5?

Ok....you have gotten this far correctly (and I am going to insert some GROUPING SYMBOLS to clarify things):

[-16 + sqrt(196)] / 6

sqrt(196) is 14.....

[-16 + 14] / 6

Now, there are TWO arithmetic problems represented by that numerator: -16 + 14 means -16 + 14 OR -16 - 14

So you've got TWO fractions: -2/6 OR -30/6....-1/3 OR -5 There's your second solution.

Apparently you have overlooked what "+" indicates.

 

[wdstone]

Ahh, you are correct, I did over look the +-. Thank you for your help!

 

[lookagain]

3x² +16x = -5

move 5 to the other side
3x² + 16x +5 = 0

plug into the quadratic formula.

-16 +- √(-16)² -4(3)(5) / 2(3) work out under the square

b = 16, not -16, so it is wrong to show \(\displaystyle (-16)^2,\)
regardless that it still equals 256.

-16 +- √196 / 6 - sqaure and add 16

+-30/6

+-5 so now I get to this.

The answer set is {-5, -1/3} How do I get to the -1/3 answer now that I have the -5?

\(\displaystyle x \ = \ \ \bigg[-16 +-\sqrt{(16)^2 - 4(3)(5)}\bigg]\bigg/[2(3)] \ \ \ or


\)



\(\displaystyle x \ = \ \ \dfrac{-16 \pm \sqrt{(16)^2 - 4(3)(5)}}{2(3)} \)