solve 3x^2-4x+5=0

Question

solve 3x^2-4x+5=0

mathmate · Answer

Do you work with complex roots?

anonymous · Answer

yes

anonymous · Answer

you may use the quadratic equation to solve for x

luigi0210 · Answer

Use the quadratic formula:
$$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$
In your equation: 3x^2-4x+5, the a=3, -4=b, and 5=c.
Just plug those into the formula and evaluate:
$$\frac{4 \pm \sqrt{(-4)^2-4(3)(5)}}{2(3)}$$
Simplify it down and you get this:
$$\frac{4 \pm \sqrt{16-60}}{6}$$
$$\frac{4 \pm \sqrt{-44}}{6}=\frac{4 \pm i \sqrt{4*11}}{6}=\frac{4 \pm 2i \sqrt{11}}{6}$$
Can you finish it from here?

anonymous · Answer

you may also complete the square (which is the longer way, but gives you good practice using completing the square method)

anonymous · Answer

when I complete the square I get a different answer... is that okay??

luigi0210 · Answer

Show us your steps

anonymous · Answer

no you should have the same results regardless of the method :-)

anonymous · Answer

i'm going to upload my work for completing the square is that okay?

anonymous · Answer

attachment

anonymous · Answer

hope my work makes sense

anonymous · Answer

yes, i am trying to get my file to upload.. but my connection is not that great

anonymous · Answer

why is the 5 not messed with when you factor out the three
in the beginning?

luigi0210 · Answer

Yea, you're suppose to move that to the other side

anonymous · Answer

Ok, that would be where i messed up!

anonymous · Answer

the 5 is not "messed" with b/c you leave it alone...you don't have to necessarily move it to the other side, simply you leave it out of the parenthesis (you don't factor a 3 from it, since it's not necessary