# In the equation, x-sqrt(x-4)=4, how do we solve for x, showing the complete solution? Thanks

Oct 10, 2017

x = 4 0r 5

#### Explanation:

Rewrite the equation as, $- \sqrt{x - 4} = 4 - x$

squaring both sides, we get
${\left[- \sqrt{x - 4}\right]}^{2} = {\left(4 - x\right)}^{2}$

$\Rightarrow x - 4 = 16 - 8 x + {x}^{2}$

$\Rightarrow {x}^{2} - 8 x - x + 16 + 4 = 0$

$\Rightarrow {x}^{2} - 9 x + 20 = 0$

$\Rightarrow {x}^{2} - 4 x - 5 x + 20 = 0$

$\Rightarrow x \left(x - 4\right) - 5 \left(x - 4\right) = 0$

$\Rightarrow \left(x - 4\right) \left(x - 5\right) = 0$

$\Rightarrow \left(x - 4\right) = 0 \mathmr{and} \left(x - 5\right) = 0$

$\Rightarrow x = 4 \mathmr{and} 5$