6x^2-29x+20=0
Answer in fraction grouping equation, step by step please
^ = square
X = variable
Answers
Answer:
2.1 Factoring 6x2-29x+20
The first term is, 6x2 its coefficient is 6 .
The middle term is, -29x its coefficient is -29 .
The last term, "the constant", is +20
Step-1 : Multiply the coefficient of the first term by the constant 6 • 20 = 120
Step-2 : Find two factors of 120 whose sum equals the coefficient of the middle term, which is -29 .
-120 + -1 = -121
-60 + -2 = -62
-40 + -3 = -43
-30 + -4 = -34
-24 + -5 = -29 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -24 and -5
6x2 - 24x - 5x - 20
Step-4 : Add up the first 2 terms, pulling out like factors :
6x • (x-4)
Add up the last 2 terms, pulling out common factors :
5 • (x-4)
Step-5 : Add up the four terms of step 4 :
(6x-5) • (x-4)
Which is the desired factorization
Equation at the end of step
2
:
(x - 4) • (6x - 5) = 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.
Solving a Single Variable Equation:
3.2 Solve : x-4 = 0
Add 4 to both sides of the equation :
x = 4
Step-by-step explanation: