Solve for x

x\in (-\infty,-5]\cup [5,\infty)

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x^{2}\geq \frac{50}{2}

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

x^{2}\geq 25

Divide 50 by 2 to get 25.

x^{2}\geq 5^{2}

Calculate the square root of 25 and get 5. Rewrite 25 as 5^{2}.

|x|\geq 5

Inequality holds for |x|\geq 5.

x\leq -5\text{; }x\geq 5

Rewrite |x|\geq 5 as x\leq -5\text{; }x\geq 5.