Lets resolve into factors 1/4x^2 - 1/81
Answers
Answer:
Step-by-step explanation:
Step by Step Solution
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(4*x-1)^2-(81)=0
Step by step solution :
STEP1:
1.1 Evaluate : (4x-1)2 = 16x2-8x+1
STEP2:Pulling out like terms
2.1 Pull out like factors :
16x2 - 8x - 80 = 8 • (2x2 - x - 10)
Trying to factor by splitting the middle term
2.2 Factoring 2x2 - x - 10
The first term is, 2x2 its coefficient is 2 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 2 • -10 = -20
Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is -1 .
-20 + 1 = -19 -10 + 2 = -8 -5 + 4 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 4
2x2 - 5x + 4x - 10
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-5)
Add up the last 2 terms, pulling out common factors :
2 • (2x-5)
Step-5 : Add up the four terms of step 4 :
(x+2) • (2x-5)
Which is the desired factorization
Equation at the end of step2:
8 • (2x - 5) • (x + 2) = 0
STEP3: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.
Equations which are never true:
3.2 Solve : 8 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
3.3 Solve : 2x-5 = 0
Add 5 to both sides of the equation :
2x = 5
Divide both sides of the equation by 2:
x = 5/2 = 2.500
Solving a Single Variable Equation:
3.4 Solve : x+2 = 0
Subtract 2 from both sides of the equation :
x = -2