Answer
$7=x$
Work Step by Step
$\sqrt {x-3} + \sqrt{x+2} = 5$
$\sqrt {x-3} + \sqrt{x+2}-\sqrt{x+2} = 5-\sqrt{x+2}$
$\sqrt {x-3} = 5-\sqrt{x+2}$
$(\sqrt {x-3})^2 = (5-\sqrt{x+2})^2$
$(x-3) = (5-\sqrt{x+2})(5-\sqrt{x+2})$
$(x-3) = 5*5+(5)(-\sqrt{x+2})+(5)(-\sqrt{x+2})+(-\sqrt{x+2})(-\sqrt{x+2}))$
$x-3 = 25-10\sqrt{x+2}+(\sqrt{x+2})(\sqrt{x+2}))$
$x-3 = 25-10\sqrt{x+2}+x+2$
$x-3 = 27-10\sqrt{x+2}+x$
$-3 = 27-10\sqrt{x+2}$
$-3-27 = 27-10\sqrt{x+2}-27$
$-30 = -10\sqrt{x+2}$
$-30/-10 = -10\sqrt{x+2}/-10$
$3= \sqrt{x+2}$
$3^2= (\sqrt{x+2})^2$
$9=x+2$
$7=x$
$\sqrt {x-3} + \sqrt{x+2} = 5$
$\sqrt {7-3} + \sqrt{7+2} = 5$
$\sqrt 4 + \sqrt 9=5$
$2+3=5$
$5=5$ (true)
