Question

How do you solve the equation `1/3(x+4)^2-1=5`?

Answer 1

`3\sqrt{2}-4`

Explanation:

new/changed values are in `\color(indianred)(\text{this }color)`

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`1/3(x+4)^2-1=5`
add 1 to both sides (cancels out the `-1`)...
`1/3(x+4)^2=\color(indianred)(6)`
multiply both sides by 3 (cancels out the `1/3`)...
`(x+4)^2=\color(indianred)(18)`
square root both sides (cancels out square on left)...
`x+4=\color(indianred)(\sqrt{18})`
subtract 4 from both sides (cancels out the `-4`)...
`x=\sqrt{18}\color(indianred)(-4)`

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now we have the base result, `x=\sqrt{18}-4`
but this can be simplified...
`\sqrt{18}=\sqrt{\cancel{3}\cdot\cancel{3}\cdot2}=3\sqrt{2}`
therefore, your result is...

`3\sqrt{2}-4`