Question

consider (8x^2 - 48x = -104).

write the equation so that

(a = 1): (x^2 + \quadx = \quad)

Explanation:

⚡ Using what you learned: completing the square

Step 1: Divide by the leading coefficient

To rewrite the equation with a leading coefficient of \( a = 1 \), divide every term in the equation by \( 8 \):

$$ \frac{8x^2}{8} - \frac{48x}{8} = \frac{-104}{8} $$

$$ x^2 - 6x = -13 $$

Step 2: Format the equation

Express the subtraction as addition of a negative coefficient to match the template \( x^2 + \boxed{\phantom{0}}x = \boxed{\phantom{0}} \):

$$ x^2 + (-6)x = -13 $$

Answer:

\( x^2 + \boxed{-6}x = \boxed{-13} \)