Question

solve for (x) in the equation (x^2 - 4x - 9 = 29).

• (x = 2 pm sqrt{42})
• (x = 2 pm sqrt{33})
• (x = 2 pm sqrt{34})
• (x = 4 pm sqrt{42})

Explanation:

Step 1: Write the equation

$$x^2 - 4x - 9 = 29$$

Step 2: Move constant to right side

$$x^2 - 4x = 38$$

Step 3: Complete the square

$$x^2 - 4x + 4 = 38 + 4$$

Step 4: Simplify both sides

$$(x - 2)^2 = 42$$

Step 5: Take square root

$$x - 2 = \pm\sqrt{42}$$

Step 6: Solve for x

$$x = 2 \pm \sqrt{42}$$

Answer:

\(x = 2 \pm \sqrt{42}\)