<PRE><B>Question 118200</B>
The square root of [x+10] plus the square root of [x-6] equals 8.
:
{{{sqrt(x+10)}}} + {{{sqrt(x-6)}}} = 8
:
Subtract {{{sqrt(x-6)}}} from both sides:
{{{sqrt(x+10)}}} = 8 - {{{sqrt(x-6)}}}
:
Square both sides, (FOIL the right side)
x + 10 = 64 - 8{{{sqrt(x-6)}}} - {{{sqrt(x-6)}}} + (x-6)
:
x + 10 = 64 - 6 - 16{{{sqrt(x-6)}}} + x
:
x + 10 = 58 + x - 16{{{sqrt(x-6)}}}
:
x - x + 10 - 58 = 16{{{sqrt(x-6)}}}
:
-48 = -16{{{x-6)}}}
:
Square the equation again:
2304 = 256(x-6)
:
2304 = 256x - 1536
:
256x = 2304 + 1536
:
256x = 3840
:
x = 3840/256
:
x = 15
:
:
Check in the original equation
{{{sqrt(15+10)}}} + {{{sqrt(15-6)}}} = 8 
</PRE>