Respuesta :

CastleRook
the solution to the algebraic expression will be:
sqrt(1-3x)=x+3
squaring both sides we get:
1-3x=(x+3)^2
1-3x=x^2+6x+9
this can be written in quadratic form as:
x^2+6x+3x+9-1=0
x^2+9x+8=0
factorizing the above we get:
x^2+9x+8=0
x^2+x+8x+8=0
x(x+1)+8(x+1)=0
(x+8)(x+1)=0
thus;
x+1=0
x=-1
and
x+8=0
x=-8
hence the answer is x=-1 or x=-8
the correct answer is A

The solution of the given equation [tex]\sqrt{1-3x} = x + 3[/tex] are -1 and -8 and this can be determined by simplifying the given equation and then factorizing it.

Given :

Equation --- [tex]\sqrt{1-3x} = x + 3[/tex]

The following steps can be used in order to determine the solution of the given equation:

Step 1 - Write the given equation.

[tex]\sqrt{1-3x} = x + 3[/tex]

Step 2 - Square on both sides in the above equation.

[tex](\sqrt{1-3x})^2 = (x + 3)^2[/tex]

Step 3 - Simplify the above equation.

[tex]1-3x=x^2+9+6x[/tex]

Step 4 - Add 3x on both sides in the above equation.

[tex]1=x^2+9+6x+3x[/tex]

[tex]1=x^2+9+9x[/tex]

Step 5 - Subtract 1 on both sides in the above equation.

[tex]x^2+8+9x=0[/tex]

Step 6 - Factorize the above equation.

[tex]x^2 + 8x + x +8 = 0[/tex]

x(x + 8) + 1(x + 8) = 0

x = -1 or -8

Therefore, the correct options are B) and C).

For more information, refer to the link given below:

https://brainly.com/question/21835898

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