Gwen was asked to solve 3x^2 - 20 = 7 by factoring using the difference of squares pattern. What is/are the correct solution(s)?
A. x = 3
B. x = -3
C. x = -3, x = 3
D. x = 9, x = -9
To solve the equation 3x^2 - 20 = 7 by factoring using the difference of squares pattern, we can first rewrite the equation as 3x^2 - 27 = 0. The difference of squares pattern states that x^2 - a^2 = (x + a)(x - a). In this case, a^2 = 27 and a = √27 = 3√3. So, the equation can be factored as (x + 3√3)(x - 3√3) = 0.
Setting each factor equal to zero, we get the solutions:
x + 3√3 = 0
x = -3√3
x - 3√3 = 0
x = 3√3
Therefore, the correct solutions are x = -3√3 and x = 3√3.
Since √3 is an irrational number, the simplified solutions are:
x ≈ -5.20 and x ≈ 5.20
So, the correct solution(s) is/are C. x = -3, x = 3.