Question

Solve: (3x−2)^2 − 1 = 15. Enter the exact answers.

Answer 1

x = 2 or x = -2/3

Step-by-step explanation:
`\begin{gathered} \text{Given:} \\ (3x-2)^2\text{ - 1 = 15} \end{gathered}`

To solve for x:

`\begin{gathered} \text{add 1 to both sides:} \\ (3x-2)^2\text{ - 1 +1 = 15 + 1} \\ (3x-2)^2\text{ = 16} \\ \text{square root both sides:} \\ \sqrt[]{(3x-2)^2}\text{ = }\pm\sqrt[]{16} \end{gathered}`
`\begin{gathered} 3x\text{ - 2 = }\pm4 \\ 3x\text{ = 2 }\pm4 \\ 3x\text{ = 2+4 }or\text{ }3x\text{ = 2 - 4} \\ 3x\text{ = 2 + 4} \\ 3x\text{ = 6} \\ x\text{ = 6/3} \\ x\text{ = 2} \end{gathered}`
`\begin{gathered} 3x\text{ = 2 - 4} \\ 3x\text{ = -2} \\ x\text{ = -2/3} \\ \\ \text{Hence, x = 2 or x = -2/3} \end{gathered}`