Using factorization method, completing the square method, general formula solve 21v = 8v {}^(2) - 9 = 0.

Question

Using factorization method, completing the square method, general formula solve
`21v = 8v {}^(2) - 9 = 0`.

Answer 1

v = -
`(3)/(8)` , v = 3

Explanation:

given

21v = 8v² - 9 = 0 , that is

8v² - 21v - 9 = 0

solving by the factorisation method

consider the factors of the product of the coefficient of the v² term and the constant term which sum to give the coefficient of the v- term

product = 8 × - 9 = - 72 and sum = - 21

the factors are - 24 and + 3

use these factors to split the v- term

8v² - 24v + 3v - 9 = 0 ( factor the first/second and third/fourth terms )

8v(v - 3) + 3(v - 3) = 0 ← factor out (v - 3) from each term

(v - 3)(8v + 3) = 0 ← in factored form

equate each factor to zero and solve for v

v - 3 = 0 ( add 3 to both sides )

v = 3

8v + 3 = 0 ( subtract 3 from both sides )

8v = - 3 ( divide both sides by 8 )

v = -
`(3)/(8)`

solutions are v = -
`(3)/(8)` and v = 3