# How do you factor and solve -1x^2 -2x+35=0?

May 26, 2016

$x = 5$ or $x = - 7$

#### Explanation:

To solve $- 1 {x}^{2} - 2 x + 35 = 0$, we should first factorize the polynomial $- 1 {x}^{2} - 2 x + 35$

To factorize a quadratic polynomial of type $a {x}^{2} + b x + c$,

one needs to split middle term $b$ in two parts whose product is $a c$. As in $- 1 {x}^{2} - 2 x + 35$, the product is $- 35$, middle term $- 2$ can be split in $- 7$ and $5$.

Hence, $- 1 {x}^{2} - 2 x + 35 = 0$ can be written as

$- 1 {x}^{2} - 7 x + 5 x + 35 = 0$

or $- x \left(x + 7\right) + 5 \left(x + 7\right) = 0$

or $\left(- x + 5\right) \left(x + 7\right) = 0$

i.e. $- x + 5 = 0$ or $x + 7 = 0$

i.e. $x = 5$ or $x = - 7$