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As follows,

Step-by-step explanation:

You can solve these either by factoring or using the quadratic formula or other ways,

1. x^2+2x+1=0

Factoring,

(x+1)^2=0

x+1=0

x=-1

2.y^2-y-2=0

Using quadratic formula,

(-b±√(b^2-4ac))/2a

(--1±√(-1^2-4*1*-2))/2*1

(1±√(1+8))/2

(1±√(9))/2

(1±3)/2

y=(1±3)/2

y=(1+3)/2    y=(1-3)/2  

y=4/2          y=-2/2

y=2              y=-1

3.y^2+y+1=0

Using quadratic formula,

(-b±√(b^2-4ac))/2a

(-1±√(1^2-4*1*1))/2*1

(-1±√(1-4))/2

(-1±√(3))/2

No real roots

4. x^2+9x+18=0

Using quadratic formula,

(-9±√(9^2-4*1*18))/2*1

(-9±√(81-72))/2

(-9±√(9))/2

(-9±3)/2

x=(-9+3)/2  x= (-9-3)/2

x=-6/2         x=-12/2

x=-3           x=-6

5.x^2+5x+6=0

Using quadratic formula,

(-5±√(b^2-4ac))/2a

(-5±√(5^2-4*1*6))/2*1

(-5±√(25-24)/2

(-5±1)/2

x=(-5+1)/2  x=(-5-1)/2

x=-4/2       x=-6/2

x=-2         x=-3

6. 3n^2-13n-10=0

Using quadratic formula,

(-b±√(b^2-4ac))/2a

(-(-13)±√(-13^2-4*3*(-10)))/2*3

(13±√(169-(-120))/6

(13±√289)/6

The discriminant b^2−4ac>0

So there are 2 real roots.

x=(13±17)/6

x=30/6 or x=-4/6

x=5 or x=-2/3

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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