Answer:
x=-1
Step-by-step explanation:
First we can square both sides to remove the square roots:
[tex](\sqrt{x+7})^{2} +(\sqrt{x+2})^{2} = (\sqrt{6x+13})^{2}[/tex]
Simplify:
[tex]x+7+x+2=6x+13[/tex]
Now we simplify further:
[tex]2x+9=6x+13[/tex]
Now we subtract 13 from both sides:
[tex]2x+9-13=6x+13-13[/tex]
Simplify:
[tex]2x-4=6x[/tex]
Subtract 2x from both sides:
[tex]2x-4-2x=6x-2x[/tex]
Simplify:
[tex]-4=4x[/tex]
Divide both sides by 4:
[tex]\frac{-4}{4} = \frac{4x}{4}[/tex]
Simplify:
-1=x
x=-1