Answer
$x=4$ satisfies the given conditions
Work Step by Step
$y=x+\sqrt{x+5}$ and $y=7$
Substitute $y$ by $7$:
$x+\sqrt{x+5}=7$
Take $x$ to the right side:
$\sqrt{x+5}=7-x$
Square both sides of the equation:
$(\sqrt{x+5})^{2}=(7-x)^{2}$
$x+5=49-14x+x^{2}$
Take all terms to the right side:
$x^{2}-14x+49-5-x=0$
$x^{2}-15x+44=0$
Solve by factoring:
$(x-11)(x-4)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x-11=0$
$x=11$
$x-4=0$
$x=4$
Check the solutions found by plugging them into the original equation:
$x=11$
$11+\sqrt{11+5}=7$ False
$x=4$
$4+\sqrt{4+5}=7$ True
$x=4$ satisfies the given conditions
