Solve for : x

\( x^2 + 4x + 3 = -(x + 3)(x + 5). \)

Thanks help when you can :)

Creampuff Aug 13, 2020

#1**0 **

Factor L side to (x+3)(x+1) then cancel (x+3) from both sides of the equation and solve.... x+1 = - (x+5)

Guest Aug 13, 2020

#2

#4**0 **

Not sure why you say it is incorrect,

if you solve as instructed: x+1 = - (x+5) you will find x = -3

I think YOU are incorrect... thanx for not really trying though !

Guest Aug 13, 2020

#5**+2 **

You can only cancel x+3 from borh sides (i.e. divide both sides by x+3) as long as x+3 is not zero. Here, x+3 turns out to be zero.

Fortuitously, you still get the right answer in this case! However, performing mathematically illegal operations is not valid, whatever the apparent result.

Alan
Aug 13, 2020

#3**0 **

Solve for x:

x^2 + 4 x + 3 = -(x + 3) (x + 5)

Expand out terms of the right hand side:

x^2 + 4 x + 3 = -x^2 - 8 x - 15

Add x^2 + 8 x + 15 to both sides:

2 x^2 + 12 x + 18 = 0

Divide both sides by 2:

x^2 + 6 x + 9 = 0

Write the left hand side as a square:

(x + 3)^2 = 0

Take the square root of both sides:

x + 3 = 0

Subtract 3 from both sides:

**x = -3**

Guest Aug 13, 2020