Solve by completing the square 3x2+3x-15=0

Question

Solve by completing the square
3x2+3x-15=0

Answer 1

3x^2+3x-15=0

3x^2+3x=15

divide both sides by 3

x^2+x=5

take half of the coefficient of x which is 1

(1/2)*1=1/2

square 1/2 to get 1/4

add 1/4 to both sides

x^2+x+(1/4)=5+(1/4)

(x+[1/2])^2=5 1/4

(x+[1/2])^2=(21/4)

take the square root of both sides

x+(1/2)=±√(21/4)

x+(1/2)=±√21/2

x=±√21/2-1/2

x=(√21-1)/2 or x=(-1+√21)/2

x=(-√21-1)/2 or x=(-1-√21)/2

Answer 2

First you want to bring the end term to the other side of the equation. Like so

3x^2 +3x=15

Then you want to divide both sides of the equation be 3 so as to get rid of the 3 on the leading term.

x^2+x=5

Then, to complete a square you divide the middle term by 2 and square it then add that to both sides. (1/2)^2=1/4

x^2+x+1/4=21/4

this is equivalent to 

(x+1/2)^2=21/4

find the square root of both sides to remove the square

x+1/2=(21/4)^1/2

Add 1/2 to both sides

x=(21/4)^1/2 + 1/2