Question

How do you solve `(x + 7) ^ { 1/ 2} + 7= 2`?

Answer 1

`color(green)(x=18,-32`

Explanation:

`color(blue)((x+7)^(1/2)+7=2`

`rarr(x+7)^(1/2)=2-7`

`rarr(x+7)^(1/2)=-5`

We know that `color(brown)(y^(1/2)=sqrty`

`rarr+-sqrt(x+7)=-5`

The symbol `+-` means `"plus or minus"`

Take the square of both sides to remove the radical sign

`rarr+-(sqrt(x+7))^2=-5^2`

`rarr+-(x+7)=25`

Therefore,

`color(orange)(+(x+7)=25`

`color(lightblue)(-(x+7)=25`

Solve both the equations

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`rarrcolor(orange)(x+7=25`

`rarrcolor(orange)(x=25-7`

`rArrcolor(green)(x=18`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`rarrcolor(lightblue)(-x-7=25`

`rarrcolor(lightblue)(-x=25+7`

`rarrcolor(lightblue)(-x=32`

`rArrcolor(green)(x=-32`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope this helps...!!! :)