Karim's first mistake occurs at Step 1.
The original quadratic equation is \( x^2 + 5x - 24 = 0 \). When he attempts to rewrite the middle term \( 5x \), he incorrectly writes it as \( 8x + (-3x) \).
The correct way to split the term \( 5x \) for factoring would be to express it as \( 8x - 3x \) or another valid pair of factors that add up to \( 5x \).
Thus, the correct first step should have been \( x^2 + 8x - 3x - 24 = 0 \) (which also isn't valid after checking) or finding two numbers that multiply to \( -24 \) and add up to \( 5 \) (which would be \( 8 \) and \( -3 \)).
The correct grouping would have been splitting \( 5x \) as \( 8x - 3x \) and not \( 8x + (-3x) \).