solve the following equation by completing the square. 12x^2 – 48x = -39​

Question

solve the following equation by completing the square. 12x^2 – 48x = -39​

in progress 0
Trúc Chi 5 years 2021-08-22T23:14:32+00:00 2 Answers 31 views 0

Answers ( )

  1. quangkhai
    0
    2021-08-22T23:15:41+00:00
    Reply

    Answer:

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

    Step-by-step explanation:

    to understand this

    you need to know about:

    • quadratic equation
    • PEMDAS

    let’s solve:

    1. \sf divide \: both \: sides \: by \: 12 : \\ \sf {x}^{2} - 4x = - \frac{13}{4}
    2. \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
    3. \sf simplify \: addition : \\ \sf { {x}^{2} } - 4x + 4 = \frac{3}{4}
    4. \sf use \: {a}^{2} - 2ab + {b}^{2} = (a - b {)}^{2} : \\ \sf (x - 2 {)}^{2} = \frac{3}{4}
    5. \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}
    6. \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}
  2. danthu
    0
    2021-08-22T23:16:17+00:00
    Reply

    Answer:

    x = – 0.40625

    Step-by-step explanation:

    12x² – 48x = – 39​

    144x – 48x = – 39

    96x = – 39

    96x ÷ 96 = – 39 ÷ 96

    x = – 39 ÷ 96

    x = – 0.40625

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )