Question

What are the steps to solve (5x-6)^2-1=15

Answer 1

The solutions are 0.4 and 2

Step-by-step explanation

STEP 1: add 1 to both sides of the equation:

`\begin{gathered} (5x-6)^2-1+1=15+1 \\ (5x-6)^2=16 \end{gathered}`

STEP 2: take square root on both sides of the equation. Remember that the square root has two results - one positive and one negative:

`\begin{gathered} \sqrt[]{(5x-6)^2}=\pm\sqrt[]{16} \\ 5x-6=\pm4 \end{gathered}`

STEP 3: add 6 on both sides of the equation:

`5x-6+6=\pm4+6`

Here we have to start separating the results, one with +4 and the other with -4:

`\begin{gathered} 5x=4+6 \\ 5x=10 \end{gathered}`
`\begin{gathered} 5x=-4+6 \\ 5x=2 \end{gathered}`

STEP 4: divide both sides by 5:

`\begin{gathered} (5x)/(5)=(10)/(5) \\ x=2 \end{gathered}`
`\begin{gathered} (5x)/(5)=(2)/(5) \\ x=0.4 \end{gathered}`

The solutions are x = 0.4 and x = 2