Answer
$8$
Work Step by Step
$\sqrt (x-4) + \sqrt (x +1) = 5$
Squaring on both sides,
$(\sqrt (x-4) + \sqrt (x +1))^{2} = 5^{2}$
Using $(a+b)^{2}= a^{2}+2ab+b^{2}$
$x-4 +2 \sqrt (x-4) \sqrt (x +1) +x+1 = 25$
Combine like terms.
$2x+2 \sqrt (x-4) \sqrt (x +1) -3 = 25$
$2x+2 \sqrt (x-4) \sqrt (x +1) = 28$
$2(x+ \sqrt (x-4) \sqrt (x +1) )= 28$
$x+ \sqrt (x-4) \sqrt (x +1) = 14$
$ \sqrt (x-4) \sqrt (x +1) = 14-x$
Squaring on both sides,
$(x-4) (x +1) = (14-x)^{2}$
Using $(a-b)^{2}= a^{2}-2ab+b^{2}$
$x^{2}-4x+x-4=196-28x+x^{2}$
$x^{2}-3x-4=196-28x+x^{2}$
$x^{2}-3x-4-196+28x-x^{2}=0$
Combine like terms.
$25x-200=0$
$25x=200$
$x=8$
