Answer:
[tex]x = 0\; ,-\frac{3}{4}[/tex]
Step-by-step explanation:
[tex]36x^3 + 27x^2 = 0[/tex]
- Take 9x² common from the expression on L.H.S.
[tex]=> 9x^2(4x + 3) = 0[/tex]
Here, x will have 2 values :-
1) [tex]9x^2(4x + 3) = 0[/tex]
- Divide both the sides by (4x + 3)
[tex]=> \frac{9x^2(4x + 3)}{(4x+3)} = \frac{0}{4x+3}[/tex]
[tex]=> 9x^2 = 0[/tex]
- Divide both the sides by 9x
[tex]=> \frac{9x^2}{9x} = \frac{0}{9x}[/tex]
[tex]=> x = 0[/tex]
2) [tex]9x^2(4x + 3) = 0[/tex]
- Divide both the sides by 9x²
[tex]=> \frac{9x^2(4x + 3)}{9x^2} = \frac{0}{9x^2}[/tex]
[tex]=> 4x+3 = 0[/tex]
- Substract both the sides from 3
[tex]=> 4x+3 -3 = 0 - 3[/tex]
[tex]=> 4x=-3[/tex]
- Divide both the sides by 4
[tex]=> \frac{4x}{4} = \frac{-3}{4}[/tex]
[tex]=> x = -\frac{3}{4}[/tex]
