Solve for the roots of the transformed equation 1. X²+2x+1=0
2. y²-y-2=0
3. y²+y+1=0
4. x²+9x+18=0
5. x²+5x+6=0
6. 3n²-13n-10=0

#1

Given equation is x²+2x+1 = 0

➝ (x)² +2(x)(1) + 1² = 0

➝ (x+1)² = 0

➝ (x+1)(x+1) = 0

➝ (x+1) = 0 or (x+1) = 0

➝ x = -1

The roots are -1 and -1

#2

Given equation is y²-y-2 = 0

➝ y²+y-2y-2 = 0

➝ y(y+1)-2(y+1) = 0

➝ (y+1)(y-2) = 0

➝ y+1 = 0 or y-2 = 0

➝ y = -1 or y = 2

The roots are -1 and 2

#3

Given equation is x²+9x+18 = 0

➝ x²+9x = -18

➝ x²+2(9x)/2 = -18

➝ x²+2(x)(9/2) = -18

On adding (9/2)² both sides then

➝ x²+2(x)(9/2)+(9/2)² = -18+(9/2)²

➝ [x+(9/2)]² = -18+(81/4)

➝ [x+(9/2)]² = (-72+81)/4

➝ [x+(9/2)]² = 9/4

➝ x+(9/2) = ±√(9/4)

➝ x+(9/2) = ±3/2

➝ x = (±3/2) -(9/2)

➝ x = (3/2)-(9/2) or -(3/2)-(9/2)

➝ x = (3-9)/2 or (-3-9)/2

➝ x = -6/2 or -12/2

➝ x = -3 or -6

The roots are -3 and -6

or x²+6x+3x+18 = 0

➝ x(x+6)+3(x+6) = 0

➝ (x+6)(x+3) = 0

➝ x+6 = 0 or x+3 = 0

➝ x = -6 or x = -3

#5

Given equation is x²+5x+6 = 0

➝ x²+2x+3x+6 = 0

➝ x(x+2)+3(x+2) = 0

➝ (x+2)(x+3) = 0

➝ x+2 = 0 or x+3 = 0

➝ x = -2 or x = -3

The roots are -2 and -3

#6

Given equation is 3n²-13n -10 = 0

➝ 3n²+2n-15n -10 = 0

➝ n(3n+2)-5(3n+2) = 0

➝ (3n+2)(n-5) = 0

➝ 3n+2 = 0 or n-5 = 0

➝ 3n = -2 or n = 5

➝ n = -2/3 or n = 5

The roots are -2/3 and 5