Question

HELP ASAP!!!

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

Table four.

Explanation:

You can rule out the first two options right away. On the LHS you have a positive number, or at best zero. On the RHS you have a negative number. Neither can happen with real numbers.

Table three doesn't work either. In order to write the LHS as a square you need to have the sum of two squares, plus twice their product. 26 is obviously not a square, so no good.

Finally, the fourth one is correct. 25 is 5 squared, and 10x is 2 times 5 times x.

Answer 2

last choice

Explanation:

x² + 10x + 24 = 0

For the middle term coefficient of 10, we need (10/2)² = 5² = 25.

x² + 10x + 25 - 1 = 0

x² + 10x + 25 = 1

(x + 5)² = 1

Answer: last choice