solve by completing the square. y square 2+8y+41=0

Question

solve by completing the square y∧2+8y+41=0

Answer 1

y²+8y+41=0

 

y² + 8y = -41

 

To complete the square, take 1/2 of the coefficient of the y term (8y) and square it = (8/2)².  You need to add it to both sides of the equation to keep things equal.

 

y² + 8y + (8/2)² = -41 + (8/2)²

 

y² + 8x + 16 = -41 + 16

 

(y+4)² = -25

 

y+4 = ±5i               [Took the square root of both sides]

 

y = -4+5i, -4-5i