Answer:
x = - 2 , x = 1
Explanation:
given the quadratic equation
x² + x + 1 = 3 ( subtract 3 from both sides )
x² + x - 2 = 0 ← in standard form
To factorise the quadratic
Consider the factors of the constant term (- 2) which sum to give the coefficient of the x- term.
the factors are + 2 and - 1 , since
+ 2 × - 1 = - 2 and + 2 - 1 = + 1
use these factors to split the x- term
x² + 2x - x - 2 = 0 ( factor the first/second and third/fourth terms )
x(x + 2) - 1 (x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(x - 1) = 0 ← in factored form
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 1 = 0 ⇒ x = 1
solutions are x = - 2 , x = 1