Question

Solve. (3x-4)^2-1=24

Answer 1

`x_(1) = - (1)/(3) \: \: . \: \: x_(2) = 3`

Explanation:

`(3x - 4 {)}^(2) - 1 = 24 \\ 9 {x}^(2) - 24x + 16 - 1 = 24 \\ 9 {x}^(2) - 24x + 15 = 24 \\ 9 {x}^(2) - 24x + 15 - 24 = 0 \\ 9 {x}^(2) - 24x - 9 = 0 \\ 3 {x}^(2) - 8x - 3 = 0 \\ x = \frac{ - ( - 8) \pm \sqrt{( - 8 {)}^(2) - 4 * 3 * ( - 3) } }{2 * 3} \\ x = (8 \pm √(64 + 36) )/(6) \\ x = (8 \pm √(100) )/(6) \\ x = (8 \pm 10)/(6) \\`

`{\boxed{Answer:{\boxed{\green{x_(1) = - (1)/(3) \: \: x_(2) = 3}}}}}`

Answer 2

`\dashrightarrow \: { \tt{ {(3x - 4)}^(2) - 1 = 24 }} \\ \\ { \tt{ {(3x - 4)}^(2) = 24 + 1}} \\ \\ { \tt{ {(3x - 4)}^(2) = 25 }} \\ \\ { \tt{ {(3x - 4)}^(2) = {5}^(2) }}`

• take a square root on either sides:

`{ \tt{ \sqrt{ {(3x - 4)}^(2) } = \sqrt{ {5}^(2) } }} \\ \\ { \tt{3x - 4 = ±5}} \\ \\ { \tt{3x =± 5 + 4}} \\ \\ { \tt{3x = 9}}`

and: 3x = -1

• divide either sides by 3:

`\dashrightarrow \: { \boxed{ \boxed{ \tt{ \: \: x = 3 \: and\:-⅓ }}}}`