Question

Express 5x²-15x+1 in the form p(x+q)²+r, where p,q,r ate constants

Answer 1

`5\bigg(x-(3)/(2)\bigg)^2-(41)/(4)`

Explanation:

• 
  `5x^2-15x +1`

• 
  `= 5\bigg(x^2-3x +(1)/(5)\bigg)`

• 
  `=5\bigg[x^2-2.(3)/(2)x +\bigg((3)/(2)\bigg)^2-\bigg((3)/(2)\bigg)^2+(1)/(5)\bigg]`

• 
  `=5\bigg[\bigg(x-(3)/(2)\bigg)^2+(1)/(5)-(9)/(4)\bigg]`

• 
  `=5\bigg[\bigg(x-(3)/(2)\bigg)^2+(4-45)/(20)\bigg]`

• 
  `=5\bigg(x-(3)/(2)\bigg)^2-5.(41)/(20)`

• 
  `=5\bigg(x-(3)/(2)\bigg)^2-5.(41)/(20)`

• 
  `=5\bigg(x-(3)/(2)\bigg)^2-(41)/(4)`