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Aloiza [94]
3 years ago
14

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

Mathematics
2 answers:
daser333 [38]3 years ago
7 0

Answer:

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

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • quadratic equation
  • PEMDAS
<h3>let's solve:</h3>
  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}
dsp733 years ago
5 0

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

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