Question

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

Answer 1

Answer:

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

• 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:

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

Answer 2

Answer:

$x_{1} = - \frac{1}{3} \: \: . \: \: x_{2} = 3$

Step-by-step explanation:

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

${\boxed{Answer:{\boxed{\green{x_{1} = - \frac{1}{3} \: \: x_{2} = 3}}}}}$