The extraneous solution is x=-1 and x=-6
Step-by-step explanation:
Given the question as;
[tex]\sqrt{-3x-2} =x+2[/tex]
Eliminate the root in the left hand side
[tex](\sqrt{-3x-2}) =x+2\\\\\\(\sqrt{-3x-2} )^2=(x+2)^2\\\\-3x-2=x^2+4x+4\\\\0=x^2+4x+3x+4+2\\\\\\0=x^2+7x+6[/tex]
solve the quadratic equation by factorization
Find multiples of 6 that add up to 7-------- 1*6
Rewrite the equation as;
x²+7x+6=0
x²+6x+x+6=0
x(x+6) +1 (x+6) =0
(x+1)(x+6) =0
x+1=0
x=-1
or
x+6=0
x=-6
The roots are, x=-1, and x=-6
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Quadratic equations : https://brainly.com/question/1332667
Keywords : extraneous, solution
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