s^2\,-\,2s\,-\,35\,=\,0
We’re asked to solve for s.
This is a quadratic equation.
The best way to solve this as it’s equal to 0 is to factor the left-hand side, and then think about the fact that those binomials that you factor into, that they have to be equal to 0.
There’s also a shortcut if you have 1 as coefficient – s2.
1 – Things about numbers that would be equal to -2 when added, but -35 when multiplied.
a\,+\,b\,=\,-2\\a\,*\,b\,=\,-35\\5\,+\,-7\,=\,-2\\5\,*\,-7\,=\,-35
2 – Now we group it.
s^2\,+\,5s\,-\,7s\,-35\,=0\\s(s+5)\,-7(s+5)\,=\,0
3 – Now we have two terms with (s+5) as a factor, undistributing s+5.
(s+5)(s-7)\,=\,0
4 – Now, either or both these two terms is/are equal to 0.
s+5=0\\s\cancel{+5-5}=\cancel0-5\\s=-5\\s-7=0\\s\,\cancel{-7+7}\,=\,\cancel0\,+7\\s=7The Formula
A*B=0\\(x+a)(x+b)\\x^2+bx+ax+ab\\x^2+(a+b)x+ab
Following the formula above, we can just do straight:
(s+5)(s-7)
