Answer:
see explanation
Step-by-step explanation:
(13)
v² - 11v + 18 = 0 ← in standard form
(v - 2)(v - 9) = 0 ← in factored form
Equate each factor to zero and solve for v
v - 2 = 0 ⇒ v = 2
v - 9 = 0 ⇒ v = 9
solutions are v = 2, v = 9
(14)
5x² - 12x + 7 = 0
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 5 × 7 = 35 and sum = - 12
The factors are - 5 and - 7
Use these factors to split the x- term
5x² - 5x - 7x + 7 = 0 ( factor the first/second and third/fourth terms )
5x(x - 1) - 7(x - 1) = 0 ← factor out (x - 1) from each term
(x - 1)(5x - 7) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
5x - 7 = 0 ⇒ 5x = 7 ⇒ x = [tex]\frac{7}{5}[/tex]
solutions are x = 1, x = [tex]\frac{7}{5}[/tex]