Solve x² - 7x + 12 = 0 — x = 3 or x = 4

Problem

$x^2 - 7x + 12 = 0$

Step-by-step solution

Find two numbers that multiply to $12$ and add to $-7$ .
Both must be negative (product positive, sum negative): $-3$ and $-4$ work since $(-3)(-4) = 12$ and $-3 + (-4) = -7$ .
Factor: $(x - 3)(x - 4) = 0$ .
Set each factor to zero: $x = 3$ or $x = 4$ .

Answer

$x = 3 \quad \text{or} \quad x = 4$

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