Question

solve square(x+5) = square(x^2-15)

Answer 1

Does "square(...)" mean square root of "..."?

Answer 2

yes sorry @SithsAndGiggles

Answer 3

\[\begin{align*}
\sqrt{x+5}&=\sqrt{x^2-15}\\
x+5&=x^2-15\\
x^2-x-20&=0
\end{align*}\]

Answer 4

Left side can be factored

Answer 5

(x-5)(x+4) @SithsAndGiggles

Answer 6

Yep.
\[(x-5)(x+4)=0~\Rightarrow~x=\cdots\]

Answer 7

4? @SithsAndGiggles

Answer 8

since it cant be negative right

Answer 9

For the left equation to be true, you must have either
\[x-5=0~~~\text{or}~~~x+4=0\]
Or equivalently, \(x=5\) or \(x=-4\).

The 4 can be negative because when you plug it into the original equation, you have
\[\sqrt{-4+5}=\sqrt{(-4)^2-15}\\
\sqrt{1}=\sqrt{16-15}\\
1=1\]

Answer 10

thank you! @SithsAndGiggles

Answer 11

you're welcome!