Respuesta :

mhanifa

Answer:

  • See below

Step-by-step explanation:

Given equation:

  • 3x² + 5x + 2 = 0

Factorize it in steps:

  • 3x² + 5x + 2 = 0
  • 3x² + 3x + 2x + 2 = 0
  • 3x(x + 1) + 2(x + 1) = 0
  • (x + 1)(3x + 2) = 0

The roots are:

  • x + 1 = 0 ⇒ x = - 1
  • 3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - 2/3

[tex]\\ \tt\hookrightarrow 3x^2+5x+2=0[/tex]

  • Split the middle term

[tex]\\ \tt\hookrightarrow 3x^2+3x+2x+2=0[/tex]

  • Take commons

[tex]\\ \tt\hookrightarrow 3x(x+1)+2(x+1)=0[/tex]

[tex]\\ \tt\hookrightarrow (3x+2)(x+1)=0[/tex]

[tex]\\ \tt\hookrightarrow x=\dfrac{-2}{3}\:or\:x=-1[/tex]

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