Question

Solve by completing the square:

y² − 5y − 6 = 0

Answer 1

Given:

y² − 5y − 6 = 0

Move the constant to the other side

y² − 5y = 6

To complete the square:

Coefficient of y = −5

Half of −5 = `-5/2`

Square of `-5/2 = 25/4`

`y^2 - 5y + 25/4 = 6 + 24/4`

Convert 6 to fourths:

`6 = 24/4`

`=> 24/4 + 25/4 = 49/4`

`(y - 5/2)^2 = 49/4`

Take square root on both sides

`y - 5/2 = +-7/2`

Solve for y

`y - 5/2 = 7/2`

`=> y = 5/2 + 7/2 = 12/2 = 6`

`y - 5/2 = 7/2`

`=> y - 5/2 = -7/2`

`=> y = 5/2 - 7/2 = (-2)/2 = -1`

y = 6 or y = −1​