SOLUTION: y^2+6y+10=0 solve by completing the square

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: y^2+6y+10=0 solve by completing the square      Log On


   

Question 486050: y^2+6y+10=0 solve by completing the square
Found 2 solutions by nerdybill, MathTherapy:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
y^2+6y+10=0
y^2+6y = -10
take 1/2 'b', square it and add to both sides:
y^2+6y+3 = -10+3
(y+3)(y+3) = -7
(y+3)^2 = -7
y+3 = sqrt(-7)
y = sqrt(-7) - 3
y = +-sqrt(-7) - 3
Note: solution is imaginary (not real)

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
y^2+6y+10=0 solve by completing the square

y%5E2+%2B+6y+%2B+10+=+0

y%5E2+%2B+6y+=+-10 ----- Subtracting "c"

y%5E2+%2B+6y+%2B+9+=+-+10+%2B+9 ------ Halving "b, squaring it, and then adding the result to both sides of equation

%28y+%2B+3%29%5E2+=+-+1

sqrt%28%28y+%2B+3%29%5E2%29+=+_%2B-sqrt%28-1%29 ----- taking square root of each side

y+%2B+3+=+_%2B-i

y+=+-+3%2B-i ---- Subtracting 3 from each side

highlight_green%28y+=+-+3%2B-i%29 ----- highlight_green%28y+=+-+3+%2B+i%29 or highlight_green%28y+=+-+3+-+i%29