Question

write two numbers that multiply to the value on top and add to the value on bottom. 4 + × -32

Explanation:

Step1: Let the two numbers be $x$ and $y$.

We know that $xy=- 32$ and $x + y=4$. From $x + y=4$, we can get $y = 4 - x$.

Step2: Substitute $y = 4 - x$ into $xy=-32$.

$x(4 - x)=-32$. Expand it to get $4x-x^{2}=-32$, or $x^{2}-4x - 32=0$.

Step3: Factor the quadratic - equation.

For the quadratic equation $x^{2}-4x - 32=0$, we need to find two numbers that multiply to - 32 and add up to - 4. The numbers are - 8 and 4. So, $x^{2}-4x - 32=(x - 8)(x + 4)=0$.

Step4: Solve for $x$.

Setting each factor equal to zero gives $x-8 = 0$ or $x + 4=0$. So, $x = 8$ or $x=-4$.
If $x = 8$, then $y=4 - 8=-4$. If $x=-4$, then $y=4-(-4)=8$.

Answer:

8 and - 4