Question

6. What is the solution?
1/2x^2–x+5=0

possible answers:
1 ± i sqrt 11
–1 ± i sqrt 9
1 ± i sqrt 9
–1 ± i sqrt 11


i would like step by step maybe to help me through this

Answer 1

i take it this is
\[\frac{1}{2}x^2-x+5=0\]
if so make your life easier and multiply by 2 first, to get
\[x^2-2x+10=0\] then it is much nicer
you can either use the quadratic formula, or since \(-2\) is even it is simpler to complete the square

Answer 2

you would start by subtracting 10 from both sides and write
\[x^2-2x=-10\] than complete the square by taking half of 2 which is 1, and write
\[(x-1)^2=-10+1=-9\] take the square root, get
\[x-1=\pm\sqrt{-9}\]
\[x-1=\pm3i\] and finally
\[x=1\pm3i\]

Answer 3

i see in your answer choices you have \(1\pm i\sqrt{9}\) but no one write \(\sqrt{9}\) since it is clearly 3

Answer 4

thank you soooo much! that helped out A LOT