Question

Can you check my quadratic equation answer?
The question was:
Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring.
−b b^2 − 4ac 2a
Use the part of the quadratic formula that you chose above and find its value given the following quadratic equation:

2x2 + 7x + 3 = 0
Numerical Answers Expected!

For the first part, I figured that b^2 − 4ac was correct. For my answer I had:

x = -7±√ ̅7^2 - 4 * 2 * 3 / 2 * 2
= -7±√ ̅49 - 24 /4
= -7±√ ̅25 /4
= -7 + 5 /4 = -2/4 = -1/2
x = -1/2

Also, since it says Numeral Answers Expected, do you think I should put x = -1/2 or just -1/2? It's online, so it will automatically mark it right or wrong.

Answer 1

well for \[2x^2 + 7x + 3 = 0\] there are two solutions.
You did get one, \[x = - \frac{ 1 }{ 2 }\]
Now what is the other solution?

Answer 2

\[x = \frac{ -7\pm \sqrt{7^2 - 4(2)(3)} }{ 2(2) }\]

Answer 3

\[\frac{ -7 \pm \sqrt{49 - 24} }{ 4 }\]

Answer 4

\[\frac{ -7 \pm \sqrt{25} }{ 4 }\]

Answer 5

\[\frac{ -7 \pm 5 }{ 4 }\]

Answer 6

\[x = \frac{ -7 + 5 }{ 4 }\]

Answer 7

-6?

Answer 8

\[\frac{ -7 + 5 }{ 4 } = \frac{ -2 }{ 4 } = \frac{ -1 }{ 2 }\]

Answer 9

\[x = \frac{ -7 - 5 }{ 4 } = \frac{ -12 }{ 4 } = -3 \]

Answer 10

Therefore,
\[x = -\frac{ 1 }{ 2 }\]
\[x = -3 \]

Answer 11

Oh, that was tricky! Thanks for the explanation!

Answer 12

yeah, no problem :)