Factor & Finding Zeros

x^{2} + 12x+35=0

x = - 7, x = - 5

Step-by-step explanation:

To factorise the quadratic

Consider the factors of the constant term ( + 35) which sum to give the coefficient of the x - term ( + 12)

The factors are + 7 and + 5, since

7 * 5 = 35 and 7 + 5 = 12, hence

x² + 12x + 35 = 0 ← in standard form

(x + 7) (x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x + 5 = 0 ⇒ x = - 5