Use the method of completing the square to solve y²+y-7=0

y=sqrt (29) / 2-1/2, - sqrt (29) / 2-1/2

Step-by-step explanation:

y^2+y-7=0

completing the square,

(b/2) ^2 = (1/2) ^2=1/4

(y+1/2) ^2=7+1/4

(y+1/2) ^2=28/4+1/4

(y+1/2) ^2=29/4

y+1/2=sqrt (29/4)

y=sqrt (29/4) - 1/2

y=sqrt (29) / 2-1/2

y=-sqrt (29) / 2-1/2

y = sqrt (29) / 2 - 1/2 or y = - 1/2 - sqrt (29) / 2

Step-by-step explanation:

Solve for y:

y^2 + y - 7 = 0

Add 7 to both sides:

y^2 + y = 7

Add 1/4 to both sides:

y^2 + y + 1/4 = 29/4

Write the left hand side as a square:

(y + 1/2) ^2 = 29/4

Take the square root of both sides:

y + 1/2 = sqrt (29) / 2 or y + 1/2 = - sqrt (29) / 2

Subtract 1/2 from both sides:

y = sqrt (29) / 2 - 1/2 or y + 1/2 = - sqrt (29) / 2

Subtract 1/2 from both sides:

Answer: y = sqrt (29) / 2 - 1/2 or y = - 1/2 - sqrt (29) / 2