The non-extraneous solutions are -6 and -5.
By checking these solution values in the original equation.
[tex](x+6)^{1/2}-5=x+1\\(x+6)^{1/2}=x+6\\((x+6)^{1/2})^2=(x+6)^2\\x+6=x^2+12x+36\\0=x^2+11x+30\\(-11+(11^2-4(1)(30))^{1/2})/2\\(-11+((1)^{1/2})/2\\(-11+1)/2=-5\\(-11-1)/2=-6\\((-6)+6)^{1/2}-5=(-6)+1\\(0^{1/2})-5=-5[/tex]
Thus, -6 is non-extraneous.
[tex]((-5)+6)^{1/2}-5=(-5)+1\\(1^{1/2})-5=-4\\1-5=-4\\-4=-4[/tex]
Thus, -5 is non-extraneous.
Learn more about non-extraneous solutions;
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