2(4x+1)(x-1)=-3 quadratic
Answers
Answer:
Step by step solution :
STEP
1
:
Equation at the end of step 1
(2 • (4x + 1) • (x - 1)) + 3 = 0
STEP
2
:
Equation at the end of step 2
2 • (4x + 1) • (x - 1) + 3 = 0
STEP
3
:
Trying to factor by splitting the middle term
3.1 Factoring 8x2-6x+1
The first term is, 8x2 its coefficient is 8 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 8 • 1 = 8
Step-2 : Find two factors of 8 whose sum equals the coefficient of the middle term, which is -6 .
-8 + -1 = -9
-4 + -2 = -6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and -2
8x2 - 4x - 2x - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (2x-1)
Add up the last 2 terms, pulling out common factors :
1 • (2x-1)
Step-5 : Add up the four terms of step 4 :
(4x-1) • (2x-1)
Which is the desired factorization
Equation at the end of step
3
:
(2x - 1) • (4x - 1) = 0
STEP
4
:
Theory - Roots of a product
4.1 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:
4.2 Solve : 2x-1 = 0
Add 1