SATMathematics Practice Test 1

Since $\mathit{a}=5\sqrt{2}$,one can substitute $5\sqrt{2}$ for $\mathit{a}$ in $2\mathit{a}=\sqrt{2}\mathit{x}$,giving $10\sqrt{2}=\sqrt{2}\mathit{x}$ ,
Squaring each side of $10\sqrt{2}=\sqrt{2}\mathit{x}$ gives ${\left(10\sqrt{2}\right)}^2={\left(\sqrt{2}\mathit{x}\right)}^2$,
which simplifies to $\left({10}^2\right){\left(\sqrt{2}\right)}^2={\left(\sqrt{2}\mathit{x}\right)}^2$,or $200=2\mathit{x}$.The gives $\mathit{x}=100$.
Checking $\mathit{x}=100$ in the original equation gives $2\left(5\sqrt{2}\right)-\sqrt{\left(2\right)\left(100\right)}$,
which is true since $2\left(5\sqrt{2}\right)=10\sqrt{2}$ and $\sqrt{\left(2\right)\left(100\right)}=\left(\sqrt{2}\right)\left(\sqrt{100}\right)=10\sqrt{2}$