Question

write two numbers that multiply to the value on top and add to the value on bottom.
54
×
□ □
+
-15
answer attempt 1 out of 10
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Explanation:

Step1: Let the two numbers be \( x \) and \( y \). We have two equations: \( xy = 54 \) and \( x + y = -15 \). From the second equation, \( y = -15 - x \). Substitute into the first equation: \( x(-15 - x) = 54 \).

\( -15x - x^2 = 54 \)
\( x^2 + 15x + 54 = 0 \)

Step2: Factor the quadratic equation. We need two numbers that multiply to 54 and add to 15. The factors of 54 are 1 & 54, 2 & 27, 3 & 18, 6 & 9. 6 and 9 add to 15. So the equation factors as \( (x + 6)(x + 9) = 0 \).

Step3: Solve for \( x \). \( x + 6 = 0 \) gives \( x = -6 \); \( x + 9 = 0 \) gives \( x = -9 \). Check: \( (-6) \times (-9) = 54 \) and \( -6 + (-9) = -15 \).

Answer:

-6 and -9