-7 = extraneous solution
The equation is
[tex]\sqrt{-3x - 5}[/tex] = x + 3
To find the value of x we need to square both sides of the equation
[tex](\sqrt{-3x - 5})^{2}[/tex] = [tex](x + 3)^{2}[/tex]
- 3x -5 = [tex]x^{2}[/tex] + 6x + 9
[tex]x^{2}[/tex] + 9x + 14 = 0
[tex]x^{2}[/tex] + 7x + 2x + 14 =0
x( x + 7) + 2( x + 7) = 0
(x + 7) (x + 2 ) = 0
x = -2, -7
To find the extraneous solution we have to put both the value of x in the equation.
x=-2
[tex]\sqrt{(-3 * -2) - 5}[/tex] = -2 +3
[tex]\sqrt{1}[/tex] = 1
1 = 1
x = -7
[tex]\sqrt{(-3 * -7) - 5}[/tex] = -7 +3
[tex]\sqrt{16}[/tex] = -4
4 = -4
The extraneous solution of the equation is -7 and -2 is the solution of the equation
To know more about the extraneous solution refer to the link given below:
https://brainly.com/question/12361474
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