Solve for x: x^2 + 3x = 0.?

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x(x+3)=0
x=0,-3

x(x+3)=0
x = 0 or -3 (A)

a

Question Number 1 :
For this equation u^2 + 3*u = 0 , answer the following questions :
A. Use factorization to find the root of the equation !
B. Use completing the square to find the root of the equation !

Answer Number 1 :
The equation u^2 + 3*u = 0 is already in a*x^2+b*x+c=0 form.
In that form, we can easily derive that the value of a = 1, b = 3, c = 0.

1A. Use factorization to find the root of the equation !
u^2 + 3*u = 0
( u ) * ( u + 3 ) = 0
So we have the answers u1 = 0 and u2 = -3

1B. Use completing the square to find the root of the equation !
u^2 + 3*u = 0 ,divide both side with 1
Then we get u^2 + 3*u = 0 ,
We know that the coefficient of u is 3
We have to use the fact that ( u + q )^2 = u^2 + 2*q*u + q^2 , and assume that q = 3/2 = 1.5
Next, we have to separate the constant to form u^2 + 3*u + 2.25 - 2.25 = 0
So we will get ( u + 1.5 )^2 - 2.25 = 0
Which can be turned into (( u + 1.5 ) - 1.5 ) * (( u + 1.5 ) + 1.5 ) = 0
And it is the same with ( u + 1.5 - 1.5 ) * ( u + 1.5 + 1.5 ) = 0
So we just need to add up, and get ( u ) * ( u + 3 ) = 0
The answers are u1 = 0 and u2 = -3

x (x + 3) = 0
x = 0 , x = - 3
OPTION A

x^2 + 3x = 0
x(x + 3) = 0

x = 0

x + 3 = 0
x = -3

∴ x = -3 , 0
(answer A)

It is 'a'. Factorise x^2 + 3x = 0. You get x (x + 3) = 0.

So x = 0 or (x + 3) = 0. If (x + 3) = 0, then x = -3.

So x = 0 or -3.

a.
0^2 + 3(0)=0
0 + 0 =0
and
(-3)^2 + 3(-3) =0
9 + -9 = 0

factor

x(x+3) = 0
by the zero property
either x=0 or x+3 =0
so x=0 or x = +3

so its A