Question

solve for (x) in the equation (x^2 - 10x + 25 = 35).

• (x = 5 pm 2sqrt{5})
• (x = 5 pm sqrt{35})
• (x = 10 pm 2sqrt{5})
• (x = 10 pm sqrt{35})

Explanation:

⚡ Using what you learned: factoring special products

Step 1: Recognize the perfect square trinomial

$$ x^2 - 10x + 25 = 35 $$

$$ (x - 5)^2 = 35 $$

Step 2: Take the square root of both sides

$$ x - 5 = \pm\sqrt{35} $$

Step 3: Solve for \(x\)

$$ x = 5 \pm\sqrt{35} $$

Answer:

\(x = 5 \pm\sqrt{35}\)