Question

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

Answer 1

`x=color(purple)(-1, 7)`

Explanation:

`3x^2-18x-21=0`

Factor out the GCF `3` from the equation.

`3(x^2-6x-7)`

Factor `x^2-6x-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(x+1)(x-7)=0`

Solve for `x`.

`color(blue)(x)+color(blue)1=color(blue)0`

`color(blue)x=color(blue)(-1)`

`color(red)(x)-color(red)7=color(red)0`

`color(red)x=color(red)7`

`color(purple)x=color(purple)(-1, 7)`

Answer 2

-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