Question

How do you solve `sqrt(x-7) = 7 - sqrt(x)`?

Answer 1

`x=16`

Explanation:

`color(blue)(sqrt(x-7)=7-sqrtx`

Take the square of both sides to remove the radical sign in the l.h.s

`rarr(sqrt(x-7))^2=(7-sqrtx)^2`

`rarrx-7=(7-sqrtx)^2`

Use the formula `color(brown)((a-b)^2=a^2-2ab+b^2`

`rarrx-7=7^2-2(7)(sqrtx)+sqrtx^2`

`rarrx-7=49-14sqrtx+x`

Subtract `x` both sides

`rarrcancelx-7cancel(-x)=49-14sqrtx+cancel(x-x`

`rarr-7=49-14sqrtx`

Subtract `49` both sides

`rarr-7-49=cancel49-14sqrtxcancel(-49`

`rarr-56=-14sqrtx`

Divide both sides by `-14`

`rarr(-56)/-14=(cancel(-14)sqrtx)/cancel(-14`

`rarr4=sqrtx`

Square both sides

`rarr4^2=sqrtx^2`

`color(green)(rarr16=x`