Question

consider (6x^2 - 48x = -104).

write the equation so that

(x^2 - 8x + \quad = \quad)

Explanation:

⚡ Using what you learned: completing the square

Step 1: Divide by the leading coefficient

To prepare the quadratic equation for completing the square, divide all terms by the coefficient of \( x^2 \), which is \( 6 \):

$$ 6x^2 - 48x = -174 $$

$$ x^2 - 8x = -29 $$

Step 2: Identify the missing values

The target template is:

$$ x^2 - 8x = -29 $$

Comparing this to the template \( x^2 - [ \quad ]x = [ \quad ] \):

• The coefficient of \( x \) is \( 8 \).
• The constant on the right side is \( -29 \).

Answer:

\( x^2 - 8x = -29 \)

The filled-in template is:
\( x^2 - 8x = -29 \)