Question

write two numbers that multiply to the value on top and add to the value on bottom.
-40
×
+
6
answer attempt 1 out of 2
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Explanation:

Step1: Define variables

Let the two numbers be $x$ and $y$.
We know:
$$x \times y = -40$$
$$x + y = 6$$

Step2: Rewrite second equation

Express $y$ as $y = 6 - x$.

Step3: Substitute into first equation

$$x(6 - x) = -40$$
$$6x - x^2 = -40$$
$$x^2 - 6x - 40 = 0$$

Step4: Factor the quadratic

$$(x - 10)(x + 4) = 0$$
Solutions: $x=10$ or $x=-4$.
If $x=10$, $y=6-10=-4$.
If $x=-4$, $y=6-(-4)=10$.

Step5: Verify the pair

$10 \times (-4) = -40$, $10 + (-4) = 6$.

Answer:

10 and -4