Question

solve the square root equation $sqrt{-3(2x + 3)}=x$. (1 point)
$x=-3$ and $x = 3$
$x = 3$
$x=-3$
no solution

Explanation:

Step1: Square both sides

$(\sqrt{-3(2x + 3)})^2=x^2$, which simplifies to $-6x-9 = x^2$.

Step2: Rearrange to quadratic - form

$x^2+6x + 9=0$.

Step3: Factor the quadratic equation

Using the formula $(a + b)^2=a^2+2ab + b^2$, we have $(x + 3)^2=0$.

Step4: Solve for x

Taking the square - root of both sides, $x+3 = 0$, so $x=-3$.

Step5: Check the solution

Substitute $x = - 3$ into the original equation:
The left - hand side is $\sqrt{-3(2\times(-3)+3)}=\sqrt{-3(-6 + 3)}=\sqrt{-3\times(-3)}=\sqrt{9}=3$.
The right - hand side is $x=-3$. Since $3
eq - 3$, the solution $x=-3$ is an extraneous solution.

Answer:

no solution