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

2 Answers
Apr 20, 2016

Answer:

#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)#

Apr 20, 2016

Answer:

-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