Answer:
see explanation
Step-by-step explanation:
To solve these equations equate them to zero, that is
x² - x - 42 = 0
Consider the factors of the constant term (- 42) which sum to give the coefficient of the x- term (- 1)
The factors are - 7 and + 6, since
- 7 × 6 = - 42 and - 7 + 6 = - 1 , thus
(x - 7)(x + 6) = 0
Equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x + 6 = 0 ⇒ x = - 6
Solutions are x = - 6, x = 7
---------------------------------------------------------
x² + x - 6 = 0 ← in standard form
(x + 3)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 2 = 0 ⇒ x = 2
Solutions are x = - 3, x = 2
------------------------------------------------------------
x² - 25 = 0 ( add 25 to both sides )
x² = 25 ( take the square root of both sides )
x = ± = ± 5
Solutions are x = - 5, x = 5