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

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:

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

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

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: