Question

Which of the following tables shows the correct steps to transform x2 + 10x + 24 = 0 into the form (x − p)2 = q? [p and q are integers] Step 1 x2 + 10x + 24 − 1 = 0 − 1 Step 2 x2 + 10x + 23 = −1 Step 3 (x + 5)2 = −1 Step 1 x2 + 10x + 24 − 2 = 0 − 2 Step 2 x2 + 10x + 22 = −2 Step 3 (x + 5)2 = −2 Step 1 x2 + 10x + 24 + 2 = 0 + 2 Step 2 x2 + 10x + 26 = 2 Step 3 (x + 5)2 = 2 Step 1 x2 + 10x + 24 + 1 = 0 + 1 Step 2 x2 + 10x + 25 = 1 Step 3 (x + 5)2 = 1

Answer 1

To transform the quadratic equation x^2 + 10x + 24 = 0 into the form (x - p)^2 = q, we complete the square by adding and subtracting (10/2)^2 = 25, resulting in (x + 5)^2 = 1.

Step-by-step explanation:

The question asks which of the following steps correctly transform the equation x2 + 10x + 24 = 0 into the form (x - p)2 = q, where p and q are integers. To do this, we need to complete the square. Completing the square involves rearranging the quadratic equation and then adding and subtracting the square of half the coefficient of x, which in this case is (10/2)2 = 52 = 25, to the equation. Here are the correct steps:

1. Add 25 to both sides of the equation: x2 + 10x + 24 + 25 = 0 + 25.
2. The equation becomes x2 + 10x + 49 = 25.
3. Now, factor the left side: (x + 5)2 = 25.

Therefore, the correct transformation steps are given as

• Step 1: x2 + 10x + 24 + 1 = 0 + 1
• Step 2: x2 + 10x + 25 = 1
• Step 3: (x + 5)2 = 1

Answer 2

Answer: y = (x - 5)² - 1