Respuesta :

Nayefx

Answer:

[tex]\large\boxed{\boxed{x = \begin{cases} \frac{ \sqrt{3} }{2} + 2 \\ - \frac{ \sqrt{3} }{2} + 2 \end{cases}}}[/tex]

Step-by-step explanation:

to understand this

you need to know about:

  • quadratic equation
  • PEMDAS

let's solve:

  1. [tex] \sf divide \: both \: sides \: by \: 12 : \\ \sf {x}^{2} - 4x = - \frac{13}{4} [/tex]
  2. [tex] \sf \: add \: { - 2}^{2} \: to \: both \: sides : \\ \sf { {x}^{2} } - 4x + ( - {2}^{2} ) = -\frac{13}{4} + ( { - 2}^{2} ) \\ {x}^{2} - 4x + 4 = -\frac{13}{4} + 4[/tex]
  3. [tex] \sf simplify \: addition : \\ \sf { {x}^{2} } - 4x + 4 = \frac{3}{4} [/tex]
  4. [tex] \sf use \: {a}^{2} - 2ab + {b}^{2} = (a - b {)}^{2} : \\ \sf (x - 2 {)}^{2} = \frac{3}{4} [/tex]
  5. [tex] \sf squre \: root \: both \: sides : \\ \sf \sqrt{(x - 2 {)}^{2} } = \pm \sqrt{ \frac{3}{4} } \\ \begin{cases} x - 2 = \frac{ \sqrt{3} }{2} \\x - 2 = - \frac{ \sqrt{3} }{2} \end{cases}[/tex]
  6. [tex] \sf add \: 2 \: to \: both \: sides : \\ \sf \begin{cases}x = \frac{ \sqrt{3} }{2} + 2 \\ x = - \frac{ \sqrt{3} }{2} + 2 \end{cases} \\ \therefore \: x = \begin{cases} \frac{ \sqrt{3} }{2} + 2 \\ - \frac{ \sqrt{3} }{2} + 2 \end{cases}[/tex]
akbusiness987

Answer:

[tex]x=\frac{4+\sqrt{3} }{2}[/tex]

[tex]x=\frac{4-\sqrt{3} }{2}[/tex]

Step-by-step explanation:

12x² - 48x = - 39

Add 39 to both sides.

12x² - 48x + 39 = 0

[tex]x = \frac{-(-48)±\sqrt{(-48)^{2}-4(12)(39) } }{(2)(12)}[/tex]

[tex]x=\frac{4+\sqrt{3} }{2}[/tex]

[tex]x=\frac{4-\sqrt{3} }{2}[/tex]

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