Question

Consider the steps for solving 3x2 – 42x + 9 = -5 for x by completing the square.

Step 1: 3x² – 42x = -14
Step 2:3(x² – 14x) = -14
Step 3: 3(x^2 – 14x + 49) = -14+__
What number should be added to the right side of the equation?
A) 96
B) 147
C) 225
D) 441

Answer 1

To complete the square to solve the equation 3x² - 42x + 9 = -5, add 49 to both sides of the equation.

Step-by-step explanation:

To solve the equation 3x² - 42x + 9 = -5 by completing the square, follow these steps:

1. Step 1: Subtract -14 from both sides of the equation to get 3x² - 42x = -14.
2. Step 2: Factor out the common factor of 3 from the left side of the equation to get 3(x² - 14x) = -14.
3. Step 3: Add the square of half the coefficient of x (49) to both sides of the equation to complete the square. This results in 3(x² - 14x + 49) = -14 + 49.
4. Therefore, the number that should be added to the right side of the equation is 49.