CPM Homework Help : AC Problem 12-51

Solve the following quadratic equations by completing the square, if possible. Leave your answers in exact form. Check your solution(s). Homework Help ✎
1. x² − 14x = −24
2. x² + 6x − 9 = 0
3. x² − 198x + 9797 = 0
4. x² − 9x = 15.75

Step 1 (a):

Add 49 to both sides.

x² − 14x + 49 = −24 + 49

Step 2 (a):

Simplify. (x − 7)² = 25

Step 3 (a):

Write two equations.

x − 7 = 5 x − 7 = −5

Answer (a):

x = 12 or −2

Step 1 (b):

Add 9 to both sides.

Hint (b):

Follow the steps in part (a).

Hint (c):

Follow the steps in part (b).

Answer (c):

x = 97 or 101

Hint (d):

Follow the steps in part (a).