Question

in Each diagram below right, the 2 numbers on the side of the x that are multiplied together to get the top number of the x but added together to get the bottom number of the x

Answer 1

We need to satisfy the following equations:

x*y = 13

x + y = -14

Isolating x from the first equation,

x = -14 - y

Substituting this result into the first equation,

(-14 - y)*y = 13

-14y- y*y = 13

-y² - 14y - 13 = 0

Using the quadratic formula,

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{14\pm\sqrt[]{(-14)^2-4\cdot(-1)\cdot(-13)}}{2\cdot(-1)} \\ y_{1,2}=\frac{14\pm\sqrt[]{144}}{-2} \\ y_1=\frac{14+12}{-2}=-13 \\ y_2=\frac{14-12}{-2}=-1 \end{gathered}$

Therefore, the solution is: