Question

solve for (x) in the equation (x^2 + 2x + 1 = 17).

• (x = -1 pm sqrt{15})
• (x = -1 pm sqrt{17})
• (x = -2 pm 2sqrt{5})
• (x = -1 pm sqrt{13})

Explanation:

⚡ Using what you learned: completing the square

Step 1: Recognize the perfect square trinomial

The left side of the equation is a perfect square trinomial:

$$ x^2 + 2x + 1 = (x + 1)^2 $$

Rewrite the equation:

$$ (x + 1)^2 = 17 $$

Step 2: Solve for \( x \)

Take the square root of both sides:

$$ x + 1 = \pm\sqrt{17} $$

Subtract \( 1 \) from both sides:

$$ x = -1 \pm\sqrt{17} $$

Answer:

\( x = -1 \pm\sqrt{17} \)