Question

Solve the following question

Answer 1

Answer:

x=-1

Step-by-step explanation:

First we can square both sides to remove the square roots:

$(\sqrt{x+7})^{2} +(\sqrt{x+2})^{2} = (\sqrt{6x+13})^{2}$

Simplify:

$x+7+x+2=6x+13$

Now we simplify further:

$2x+9=6x+13$

Now we subtract 13 from both sides:

$2x+9-13=6x+13-13$

Simplify:

$2x-4=6x$

Subtract 2x from both sides:

$2x-4-2x=6x-2x$

Simplify:

$-4=4x$

Divide both sides by 4:

$\frac{-4}{4} = \frac{4x}{4}$

Simplify:

-1=x

x=-1