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

Question

Isaiah Anthony · Accepted Answer

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

#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)#

Avery Alexander · Answer

-1 and 7

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

Hazel Anglin · Answer

undefined To solve the quadratic equation 3x^2 - 18x - 21 = 0, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 3, b = -18, and c = -21.

Plugging these values into the formula:

x = (18 ± √((-18)^2 - 4 * 3 * (-21))) / (2 * 3)

Simplify under the square root:

x = (18 ± √(324 + 252)) / 6

x = (18 ± √576) / 6

x = (18 ± 24) / 6

This gives two possible solutions:

x₁ = (18 + 24) / 6 = 42 / 6 = 7

x₂ = (18 - 24) / 6 = -6 / 6 = -1

So, the solutions to the equation 3x^2 - 18x - 21 = 0 are x = 7 and x = -1.