Question

How do you solve using the completing the square method `3x^2 + 2x + 5 = 0`?

Answer 1

Solution: `x =-1/3 +sqrt (14)/3* i or x =-1/3 - sqrt (14)/3* i`

Explanation:

`3x^2+2x+5 =0 or 3(x^2+2/3x) +5 =0 or 3(x^2+2/3x+(1/3)^2) -1/3+5 =0` or `3( x+1/3)^2 +14/3 =0 or ( x+1/3)^2 = -14/9 or x +1/3 = +-sqrt (-14/9)`
or `x = -1/3 +- sqrt (-14/9) :. x =-1/3 +sqrt (14)/3* i or x =-1/3 - sqrt (14)/3* i` [`i^2 = -1]`
Solution: `x =-1/3 +sqrt (14)/3* i or x =-1/3 - sqrt (14)/3* i` [Ans]