Question

solve $x^2 = 50$. simplify your answer as much as possible. if there is more than one solution, separate them with commas. $x = \square$

Explanation:

Step1: Take square root of both sides

To solve the equation \( x^2 = 50 \), we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution because \( (\pm a)^2=a^2 \). So we have \( x=\pm\sqrt{50} \).

Step2: Simplify the square root

Simplify \( \sqrt{50} \). We can factor 50 as \( 25\times2 \), and since \( \sqrt{25\times2}=\sqrt{25}\times\sqrt{2} \) (by the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) for \( a\geq0,b\geq0 \)) and \( \sqrt{25} = 5 \), we get \( \sqrt{50}=5\sqrt{2} \). So the solutions for \( x \) are \( 5\sqrt{2} \) and \( - 5\sqrt{2} \).

Answer:

\( 5\sqrt{2}, - 5\sqrt{2} \)