# How do you solve x^2 + 6x - 7 = 0?

Jul 7, 2015

Notice $x = 1$ is a root since the sum of the coefficients is $0$.
Then find the other root $x = - 7$

#### Explanation:

Let $f \left(x\right) = {x}^{2} + 6 x - 7$

First notice that the sum of the coefficients is zero: $1 + 6 - 7 = 0$
so $f \left(1\right) = 0$, $1$ is a root and $\left(x - 1\right)$ is a factor of $f \left(x\right)$.

In order to get the ${x}^{2}$ leading term and $- 7$ constant term, the other factor must be $\left(x + 7\right)$, giving the other root as $x = - 7$

${x}^{2} + 6 x - 7 = \left(x - 1\right) \left(x + 7\right)$