Question

given \\((x - 1)^2 = 50\\), select the values of \\(x\\).

\\(x = -49\\)
\\(x = 51\\)
\\(x = 1 + 5\sqrt{2}\\)
\\(x = 1 - 5\sqrt{2}\\)

Explanation:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Take the square root of both sides

$$ \sqrt{(x - 1)^2} = \pm\sqrt{50} $$

$$ x - 1 = \pm\sqrt{50} $$

Step 2: Simplify the radical

$$ \sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2} $$

$$ x - 1 = \pm 5\sqrt{2} $$

Step 3: Solve for x

$$ x = 1 \pm 5\sqrt{2} $$

This gives two solutions:

$$ x = 1 + 5\sqrt{2} $$

$$ x = 1 - 5\sqrt{2} $$

Answer:

• \( x = 1 + 5\sqrt{2} \)
• \( x = 1 - 5\sqrt{2} \)