Question 372500
You can just use sqrt(10-2x) to denote the square root function.
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{{{sqrt(10-2x)-sqrt(5x+16)=3}}}
{{{sqrt(10-2x)=sqrt(5x+16)+3}}}
Square both sides.
{{{10-2x=5x+16+6*sqrt(5x+16)+9}}}
{{{10-2x=5x+25+6*sqrt(5x+16)}}}
{{{-15-7x=6*sqrt(5x+16)}}}
{{{-(7x+15)=6*sqrt(5x+16)}}}
Square both sides again,
{{{49x^2+210x+225=36(5x+16)}}}
{{{49x^2+210x+225=180x+576)}}}
{{{49x^2+30x-351=0}}}
{{{(49x-117)(x+3)=0}}}
Two solutions:
{{{49x-117=0}}}
{{{x=117/49}}}
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{{{x+3=0}}}
{{{x=-3}}}
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Verify the solutions,
Since {{{x=117/49}}} would lead to a negative argument for the square root function, it is not a solution.
{{{highlight(x=-3)}}}
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{{{drawing(300,300,-5,5,-5,5,grid(1),circle(-3,3,0.3),graph(300,300,-5,5,-5,5,sqrt(10-2x)-sqrt(5x+16),3))}}}