Question

write two numbers that multiply to the value on top and add to the value on bottom. - 20 - 8

Explanation:

Step1: Let the two numbers be \(x\) and \(y\).

We have the equations \(xy=- 20\) and \(x + y=-8\). From \(x + y=-8\), we can express \(y=-8 - x\).

Step2: Substitute \(y=-8 - x\) into \(xy=-20\).

\(x(-8 - x)=-20\), which simplifies to \(-8x-x^{2}=-20\), or \(x^{2}+8x - 20 = 0\).

Step3: Factor the quadratic equation.

We need to find two numbers that multiply to \(-20\) and add up to \(8\). The factors of \(-20\) are \(\pm1,\pm2,\pm4,\pm5,\pm10,\pm20\). We find that \((x + 10)(x - 2)=0\).

Step4: Solve for \(x\).

Setting each factor equal to zero gives \(x+10 = 0\) or \(x - 2=0\), so \(x=-10\) or \(x = 2\).
If \(x=-10\), then \(y=-8-(-10)=2\). If \(x = 2\), then \(y=-8 - 2=-10\).

Answer:

The two numbers are \(2\) and \(-10\)