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What two numbers multiply to 45 and add to -14 ? Type your answer...

Ask by Craig Savage. in the United States
Mar 08,2025

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Tutor-Verified Answer

Answer

Los dos números son -5 y -9.

Solution

1. Sea \( a \) y \( b \) los dos números. Entonces: \[ a \times b = 45 \quad \text{y} \quad a + b = -14 \] 2. Dado que el producto es positivo y la suma es negativa, ambos números deben ser negativos. 3. Se buscan dos números negativos cuya multiplicación sea \( 45 \) y su suma sea \( -14 \). Considerando los factores de 45: - \(-1\) y \(-45\): \( -1 + (-45) = -46 \) - \(-3\) y \(-15\): \( -3 + (-15) = -18 \) - \(-5\) y \(-9\): \( -5 + (-9) = -14 \) 4. Los números \(-5\) y \(-9\) cumplen ambas condiciones. La respuesta es: \(-5\) y \(-9\).

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The Deep Dive

To solve the puzzle of two numbers that multiply to 45 and add to -14, we can think of them as two negative factors because the sum is negative. Let's denote the numbers as x and y. We need numbers that fit the equation: \(x \times y = 45\) and \(x + y = -14\). The numbers that satisfy both conditions are -9 and -5. When multiplied, they yield 45 (-9 * -5 = 45), and when added together, they give -14 (-9 + -5 = -14). So, the answer is -9 and -5!

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