Solve the following equation?

Question

x^2 + 4x + 3 = 0

Answer 1

x^2+4x+3=0

Here are some methods you can use to solve.

1) Factor.

x^2+bx+c=0

to factor, find two such numbers that:

r+s=b

rs=c

So,

x^2+rx+sx+rs=0

x(x+r)+s(x+r)=0

(x+s)(x+r)=0

x+s=0, x=-s

x+r=0, x=-r

So, b=4, c=3

r=1, s=3 is valid, therefore,

x^2+x+3x+3=0

x(x+1)+3(x+1)=0

(x+1)(x+3)=0

x+1=0, x=-1

x+3=0, x=-3

2) Complete the square.

x^2+2xy+y^2=(x+y)^2

The closest square is at y=2, so:

x^2+2xy+y^2 for y=2 is:

x^2+4x+4

We have:

x^2+4x+3

So, add 1:

x^2+4x+4=1

(x+2)^2=1

Square root both sides.

x+2=+/-sqrt1

x+2=+/-1

Subtract 2

x=-2+/-1

So,

x=-2-1=-3

x=-2+1=-1

3) Quadratic Formula

ax^2+bx+c=0

Has the solutions:

x=[-b+/-sqrt[b^2-4ac]]/2a

So, a=1, b=4, c=3

-b=-4

b^2-4ac=16-12=4--->sqrt of this is +/-2

2a=2

So,

x=[-4+/-2]/2

x=[-4/2]+/-[2/2]

x=-2+/-1

So,

x=-2+1=-1

x=-2-1=-3

4a) Graph

Graph the function:

x^2+4x+3=y

the points where it meets the x-axis is where the solutions lie (note that this will be x=-3 and x=-1)

4b) Graph

Graph the function:

x^2+4x=y

Also graph the line:

y=-3

Where the two functions meet the solution lies (x=-3 and x=-1)

4c) Graph

Graph the function:

x^2=y

Also graph the linear function:

y=-(4x+3)

Where the two meet lie the solutions (x=-3 and x=-1)

Hope this helped. Email for qs. Peace

Answer 2

factorising

(x+3)(x+1) = 0

so x = -3  or  -1.

Answer 3

(x+1)(x+3)=0

by the zero property

x+1=0 or x+3=0

so

x=-1 or x=-3

Answer 4

(x + 3) (x + 1) = 0

x = - 3 , x = - 1

Answer 5

x=-1 or x=-3

Answer 6

Using the quadratic formula you get :

x= -1, x=  -3