SOLUTION: Find the solutions of the equation. 1/2x^2-x+5=0 A) 1 [+ or -] √9i B) 1 [+ or -] √11i C) -1 [+ or -] √9i D) -1 [+ or -] √11i

Algebra ->  Equations -> SOLUTION: Find the solutions of the equation. 1/2x^2-x+5=0 A) 1 [+ or -] √9i B) 1 [+ or -] √11i C) -1 [+ or -] √9i D) -1 [+ or -] √11i      Log On


   

Question 668998: Find the solutions of the equation.
1/2x^2-x+5=0
A) 1 [+ or -] √9i
B) 1 [+ or -] √11i
C) -1 [+ or -] √9i
D) -1 [+ or -] √11i
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
expr%281%2F2%29x%5E2-x%2B5=0

2%2A%28expr%281%2F2%29x%5E2-x%2B5%29=2%2A0

x%5E2-2x%2B10=0

Use the quadratic formula to solve for x

x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%28-2%29%2B-sqrt%28%28-2%29%5E2-4%281%29%2810%29%29%29%2F%282%281%29%29

x+=+%282%2B-sqrt%284-%2840%29%29%29%2F%282%29

x+=+%282%2B-sqrt%28-36%29%29%2F2

x+=+%282%2Bsqrt%28-36%29%29%2F2 or x+=+%282-sqrt%28-36%29%29%2F2

x+=+%282%2B6%2Ai%29%2F2 or x+=+%282-6%2Ai%29%2F2

x+=+1%2B3i or x+=+1-3i

So the two solutions are x+=+1%2B3i or x+=+1-3i

For some strange reason, the book isn't showing the full simplified answers. The answer of those choices given is x+=+1%2Bsqrt%289%29%2Ai or x+=+1-sqrt%289%29%2Ai (so either A or C -- Note: the 'i' term is NOT in the square root)

Why the book did not simplify the square root of 9, I have no clue.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2%29x%5E2-x%2B5=0
0.5x%5E2-x%2B5=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A0.5%2A5+%29%29%2F%282%2A0.5%29+
x+=+%281+%2B-+sqrt%28+1-10+%29%29%2F1+
x+=+%281+%2B-+sqrt%28+-9+%29%29+... ......we can write -9 as %28-1%29%2A9
x+=+%281+%2B-+sqrt%28%28-1%29%2A9%29%29 ......we can write sqrt%28+%28-1%29%2A9+%29 as
sqrt%28+%28-1%29%2Asqrt%28+9+%29+%29

x+=+%281+%2B-+sqrt%28+%28-1%29%2Asqrt%28+9+%29+%29%29+...as you know sqrt%28-1%29=i

x+=+%281+%2B-+sqrt%289%29%2Ai%29+


so, your answer is: A