Question

What 2 numbers multiplied together equal 35 but when added egual negative 36

Answer 1

$\begin{cases} xy=35 \\ x+y=-36 \end{cases}\\\\\begin{cases} xy=35 \\ x =-36-y \end{cases}\\ \\substitution\\\\(-36-y)y=35\\\\ -36y-y^2=35$

$y^2+36y+35=0\\\\a=1, \ \ b=36, \ \ c=35\\ \\\Delta =b^2-4ac = 36^2 -4\cdot 1\cdot 35 = 1296- 140=1156\\\\y_{1}=\frac{-b -\sqrt{\Delta} }{2a}= \frac{ -36-\sqrt{1156}}{2}=\frac{-36-34}{2}=-\frac{70}{2}=-35\\\\y_{2}=\frac{-b +\sqrt{\Delta} }{2a}= \frac{-36+34}{2}=-\frac{-2}{2}=-1$

$\begin{cases} y=-35 \\ x =-36- (-35) \end{cases}\ \ \ or \ \ \ \begin{cases} y=-1 \\ x =-36- (-1) \end{cases}\\\\\\\begin{cases} y=-35 \\ x =-36+35 \end{cases}\ \ \ or \ \ \ \begin{cases} y=-1 \\ x =-36+1 \end{cases}\\\\\\\begin{cases} y=-35 \\ x =-1 \end{cases}\ \ \ or \ \ \ \begin{cases} y=-1 \\ x =-35 \end{cases}$