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

1 Answer
seol
Mar 12, 2017

3\sqrt{2}-4

Explanation:

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

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)

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

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