Question

What is the solution to

`√( - x) = √(x + 13)`
​

Answer 1

`x=-\frac{13}2`

Explanation:

`~~~~~√(-x) = √(x+13)\\\\\implies -x= x+13~~~~~~~~~~~~~~~~;[\text{Square on both sides}]\\\\\implies -x -x = 13\\\\\implies -2x = 13\\\\\implies x = -\frac{13}2\\\\\text{Verify solution:}\\\\~~~~~~~\sqrt{-\left(- \frac{13} 2 \right)} = \sqrt{-\frac{13}2 +13}\\\\\\\implies \sqrt{\frac{13}2} = \sqrt{\frac{13}2}\\\\\text{Hence, the solution is}~ x=-\frac{13}2`

Answer 2

Answer: -6.5

Explanation:

First, you take the values on both sides to the power of 2 to get:

-x = x + 13

Subtract x on both sides.

-2x = 13

Divide both sides by -2.

x = -6.5