So I've been self studying algebra 2 along with reading calculus for dummies lol, and I've recently taught myself completing the square as well as the quadratic formula, but this particular problem wants me to give two decimal answers I can't seem to find myself at.

3j2 + 8j – 2 = 0.

The explanation of the problem leaves off at:
j =
 -8 + 88 6
or
 j
=
 -8 – 88 6
^ I GOT THAT, but then I simplify the square root of 88 and end up getting: j = -8 + or - 2 * SQUAREROOTOF 22 /6 <---- THAT would be what everything I've learned has taught me to leave off at
BUT, the site that gives me the quadratic equation states the answer as: j = 0.23 or j = -2.90, (Rounded to the nearest hundredth)

HOW!!?? Thanks

ALSO, MY APOLOGIES, the square root symbol won't show for some reason.. there should be square roots over both 88's..

$\displaystyle 3j^2+8j-2=0$

$\displaystyle j=\frac{-8 \pm \sqrt{8^2-4(3)(-2)}}{2(3)} = \frac{-8 \pm \sqrt{88}}{6} = \frac{-8\pm 2\sqrt{22}}{6} =\frac{-4\pm\sqrt{22}}{3}$

Using a calculator, $j=0.23$ and $j=-2.90$

Thanks Skeeter.. but I still don't fully understand.. I think I understand that you took the common factor of 2 for everything in the equation other than what's in the square root, rendering -8 = -4, 2=1 , and 6 = 3, (I must admit the question is lingering in my head as to how you can do that SELECTIVELY, meaning why DON'T you have to do it to the square root of 22 as well? After all, the common rule is anything done to one side has to be done to the other... but putting that aside, I really still don't see how - 4 + or - SQUAREROOT of 22 / 3 gives you those decimals, specifically what do you do to get there ??

entered into a calculator ...

AHH I GET IT you took the square root of 22 in decimal form added / subtracted it to 4 and divided the sum by 3, I got both answers, thanks!

Originally Posted by keith11
AHH I GET IT you took the square root of 22 in decimal form added / subtracted it to 4 and divided the sum by 3, I got both answers, thanks!
the calculator follows the order of operations ...

it first added $-4$ and $\pm\sqrt{22}$, then it divided the result by $3$

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in quatratic equation the decimal answer

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