ANSWER
No solution
EXPLANATION
We want to find the number of solutions for
[tex] \sqrt{2x + 3} + 6 = 0[/tex]
Add -6 to both sides.
[tex] \sqrt{2x + 3} = - 6[/tex]
Square both sides
[tex]2x + 3 = 36[/tex]
Solve for x.
[tex]2x = 36 - 3[/tex]
[tex]2x = 33[/tex]
[tex]x = \frac{33}{2} [/tex]
[tex]x = 16.5[/tex]
Substitute back into the equation.
[tex] \sqrt{2(\frac{33}{2})+ 3} + 6 = 0[/tex]
[tex] \sqrt{33+ 3} + 6 = 0[/tex]
[tex] \sqrt{36} + 6 = 0[/tex]
[tex] 6+ 6 = 0[/tex]
[tex]12 = 0[/tex]
This is not true.
The equation has no solution
