Question

x×(x-5)+4=0
(x-10)×(x+10)=0

Answer 1

x²-10²=0
x²-100=0
x=√100=10

Answer 2

$\displaystyle a).x(x-5)+4=0 \\ x^2-5x+4=0 \\ a=1,b=-5,c=4 \\ \Delta=b^2-4ac=5^2-4 \cdot 1 \cdot 4=25-16=9\ \textgreater \ 0 \\ x_1= \frac{5+ \sqrt{9} }{2 \cdot 1} = \frac{5+3}{2} = \frac{8}{2} =4 \\ \\ x_2= \frac{5- \sqrt{9} }{2 \cdot 1} = \frac{5-3}{2} = \frac{2}{2} =1 \\ \\ S=\{1;4\}$

$\displaystyle b).(x-10)(x+10)=0 \\ x^2-100=0 \\ a=1,b=0,c=-100 \\ \Delta=b^2-4ac=0-4 \cdot 1 \cdot (-100)=0+400=400\ \textgreater \ 0 \\ x_1= \frac{0+ \sqrt{400} }{2 \cdot 1} = \frac{0+20}{2} = \frac{20}{2} =10 \\ \\ x_2= \frac{0- \sqrt{400} }{2 \cdot 1} = \frac{0-20}{2} = \frac{-20}{2} =-10 \\ \\ S=\{-10;10\}$