Question 604223
{{{sqrt(10x-4)+sqrt(16x+17)=sqrt(75x-29)}}}



Square both sides


{{{10x-4 +2sqrt(10x-4)*sqrt(16x+17)+16x+17 = 75x-29}}}


{{{26x+13 +2sqrt(10x-4)*sqrt(16x+17)= 75x-29}}}


{{{2sqrt(10x-4)*sqrt(16x+17)= 49x-42}}}

square both sides

{{{4(10x-4)(16x+17)=(49x-42)^2}}}


{{{4(160x^2+170x-64x-78)=(49x-42)^2}}}


{{{4(160x^2+106x-78)=2401x^2-4116x+1764}}}


{{{640x^2+424x-312=2401x^2-4116x+1764}}}

{{{1761x^2-4540x+2076=0}}}

Find the roots of the equation by quadratic formula							
							
a=	1761	,	b=	-4540	,	c=	2076
							
b^2-4ac=	20611600	-14623344				
b^2-4ac=	5988256						
{{{	sqrt(	5988256	)=	2447.09	}}}		
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}							
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}							
x1=(	4540	+	2447.09	)/	3522		
x1=	1.98						
{{{x2=(-b-sqrt(b^2-4ac))/(2a)}}}							
x2=(	4540	-2447.09	) /	3522			
x2=	0.59						


(1.98,0.59)