Answer:
x =(22-√196)/6=(11-7)/3= 1.333
Step-by-step explanation:
(3x2 - 22x) + 24 = 0
The first term is, 3x2 its coefficient is 3 .
The middle term is, -22x its coefficient is -22 .
The last term, "the constant", is +24
Step-1 : Multiply the coefficient of the first term by the constant 3 • 24 = 72
Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is -22 .
-72 + -1 = -73
-36 + -2 = -38
-24 + -3 = -27
-18 + -4 = -22 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -18 and -4
3x2 - 18x - 4x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (x-6)
Add up the last 2 terms, pulling out common factors :
4 • (x-6)
Step-5 : Add up the four terms of step 4 :
(3x-4) • (x-6)
Which is the desired factorization
Equation at the end of step 2:
(x - 6) • (3x - 4) = 0
STEP 3:
Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
