Question

3x squared -42x+9=-5 for completing the square

Answer 1

`3x^2 -42x + 9 = -5`

Subtract 9 from both sides

`3x^2 -42x = -5 - 9`


`3x^2 -42x = -14`

Divide by 3 through

`x^2 -14x = - (14)/(3)`

Add (b/2)^2 to form perfect square

`x^2 -14x + ((14)/(2))^2 = - (14)/(3) + ((14)/(2))^2`

Form perfect square

`(x -7)^2 = (7)/(3)`

square root both sides

`(x -7) = \pm \sqrt{(7)/(3)}`

Add 7 to both sides

`x = \pm \sqrt{(7)/(3)} + 7`

Rewrite the answer into 2 different answers

`x = 7 + \sqrt{(7)/(3)} \ or \ 7 - \sqrt{(7)/(3)}`