Question

How would I solve this problem by completing the square?

2y squared + 2y = -1

Answer 1

2y^2 + 2y = -1

2(y^2 + y) = -1

2(y^2 + y + 1/4 - 1/4) = -1

2( (y^2 + y + 1/4) - 1/4) = -1

2( (y + 1/2)^2 - 1/4) = -1

2(y + 1/2)^2 - 2(1/4) = -1

2(y + 1/2)^2 - 2/4 = -1

2(y + 1/2)^2 - 1/2 = -1

I'll let you take over from here

Answer 2

so far I have (2y + 1\4) - 1\2 = -1

Answer 3

would I add the 1 to the left hand side so a 0 would be on the right side and then do the quadratic formula?

Answer 4

2(y + 1/2)^2 - 1/2 = -1

2(y + 1/2)^2 = -1+1/2

2(y + 1/2)^2 = -1/2

(y + 1/2)^2 = (-1/2)*(1/2)

(y + 1/2)^2 = -1/4

Answer 5

so then y = -1\2?

Answer 6

(y + 1/2)^2 = -1/4

y + 1/2 = sqrt(-1/4) or y + 1/2 = -sqrt(-1/4)

y + 1/2 = (1/2)*i or y + 1/2 = -(1/2)*i

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y = ??? or y = ???

Answer 7

so then that makes y = 1\2, -1\2, 1\2i, or -1\2i

Answer 8

no

Answer 9

but isn't the square root of 1\4 1\2?

Answer 10

y + 1/2 = (1/2)*i or y + 1/2 = -(1/2)*i

y = - 1/2 + (1/2)*i or y = - 1/2 - (1/2)*i

Answer 11

sqrt(-1/4) = (1/2)*i