Question

What is the solution to 0" id="TexFormula1" title=" \sqrt{ - x} = \sqrt{x + 13} " alt=" \sqrt{ - x} = \sqrt{x + 13} " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

$x=-\dfrac{13}2$

Step-by-step explanation:

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

Answer 2

Answer: -6.5

Step-by-step 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