Answer
$x=5$
Work Step by Step
$\sqrt {2x-1}-4=-\sqrt {x-4}$
$\sqrt {2x-1}-4+4=-\sqrt {x-4}+4$
$\sqrt {2x-1}=4-\sqrt {x-4}$
$(\sqrt {2x-1})^2=(4-\sqrt {x-4})^2$
$2x-1=4*4+4*(-\sqrt {x-4})+(-\sqrt {x-4})*4+(-\sqrt {x-4})(-\sqrt {x-4})$
$2x-1=16-8\sqrt {x-4}+(\sqrt {x-4})(\sqrt {x-4})$
$2x-1=16-8\sqrt {x-4}+(x-4)$
$2x-1=16-8\sqrt {x-4}+(x-4)$
$2x-1=16-8\sqrt {x-4}+x-4$
$2x-1+4=16-8\sqrt {x-4}+x-4+4$
$2x+3=16-8\sqrt {x-4}+x$
$x+3=16-8\sqrt {x-4}$
$x-13=-8\sqrt {x-4}$
$(x-13)^2=(-8\sqrt {x-4})^2$
$x*x+x*(-13)+(-13)*x+(-13)(-13)=(-8)^2*(\sqrt{x-4})^2$
$x^2-26x+169=64*(x-4)$
$x^2-26x+169=64x-256$
$x^2-26x+169-64x+256=64x-256-64x+256$
$x^2-90x+425=0$
$(x-85)(x-5)=0$
$x-85=0$
$x=85$
$x-5=0$
$x=5$
$\sqrt {2x-1}-4=-\sqrt {x-4}$
$\sqrt {2*85-1}-4=-\sqrt {85-4}$
$\sqrt {170-1}-4=-\sqrt {81}$
$\sqrt {169}-4=-9$
$13-4=-9$
$9=-9$ (false)
$\sqrt {2x-1}-4=-\sqrt {x-4}$
$\sqrt {2*5-1}-4=-\sqrt {5-4}$
$\sqrt {10-1}-4=-\sqrt {1}$
$\sqrt {9}-4=-1$
$3-4=-1$ (true)
