# How do you solve 3x^2-18x-21=0?

Apr 20, 2016

$x = \textcolor{p u r p \le}{- 1 , 7}$

#### Explanation:

$3 {x}^{2} - 18 x - 21 = 0$

Factor out the GCF $3$ from the equation.

$3 \left({x}^{2} - 6 x - 7\right)$

Factor ${x}^{2} - 6 x - 7$.

Find two numbers that when added equal $- 6$ and when multiplied equal $- 7$.

The numbers $- 7$ and $1$ fit the criteria.

Rewrite the equation.

$3 \left(x + 1\right) \left(x - 7\right) = 0$

Solve for $x$.

$\textcolor{b l u e}{x} + \textcolor{b l u e}{1} = \textcolor{b l u e}{0}$

$\textcolor{b l u e}{x} = \textcolor{b l u e}{- 1}$

$\textcolor{red}{x} - \textcolor{red}{7} = \textcolor{red}{0}$

$\textcolor{red}{x} = \textcolor{red}{7}$

$\textcolor{p u r p \le}{x} = \textcolor{p u r p \le}{- 1 , 7}$

Apr 20, 2016

-1 and 7

#### Explanation:

f(x) = 3y = 3(x^2 - 6x - 7) = 0
Solve the quadratic equation y = 0, in parentheses.
Since a - b + c = 0, use shortcut; the 2 real roots are: -1 and -c/a = 7.

Reminder of Shortcut
- When a + b + c = 0 --> 2 real roots: 1 and c/a
- When a - b + c = 0 --> 2 real roots: -1 and -c/a