Question

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

Answer 1

`\large\boxed{\boxed{x = \begin{cases} ( √(3) )/(2) + 2 \\ - ( √(3) )/(2) + 2 \end{cases}}}`

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 = - (13)/(4)`
2. 
   `\sf \: add \: { - 2}^(2) \: to \: both \: sides : \\ \sf { {x}^(2) } - 4x + ( - {2}^(2) ) = -(13)/(4) + ( { - 2}^(2) ) \\ {x}^(2) - 4x + 4 = -(13)/(4) + 4`
3. 
   `\sf simplify \: addition : \\ \sf { {x}^(2) } - 4x + 4 = (3)/(4)`
4. 
   `\sf use \: {a}^(2) - 2ab + {b}^(2) = (a - b {)}^(2) : \\ \sf (x - 2 {)}^(2) = (3)/(4)`
5. 
   `\sf squre \: root \: both \: sides : \\ \sf \sqrt{(x - 2 {)}^(2) } = \pm \sqrt{ (3)/(4) } \\ \begin{cases} x - 2 = ( √(3) )/(2) \\x - 2 = - ( √(3) )/(2) \end{cases}`
6. 
   `\sf add \: 2 \: to \: both \: sides : \\ \sf \begin{cases}x = ( √(3) )/(2) + 2 \\ x = - ( √(3) )/(2) + 2 \end{cases} \\ \therefore \: x = \begin{cases} ( √(3) )/(2) + 2 \\ - ( √(3) )/(2) + 2 \end{cases}`