To solve this equation, we will use the quadratic formula x = [-b ± sqrt(b² - 4ac)] / 2a. However, before plugging in the values, we need to determine the nature of roots using the discriminant, which is calculated using the formula: D = b² - 4ac.
For the given equation x² - 14 = 0, the coefficients are:
a = 1 (the coefficient of x² is 1)
b = 0 (there are no terms with x, thus b = 0)
c = -14 (the constant term is -14)
Let's first calculate the discriminant (D)
D = b² - 4ac
D = (0)² - 4*1*(-14)
D = 56
The discriminant is 56.
Now, based on the discriminant, we can determine the number and types of solutions.
If the discriminant is greater than 0, there will be two distinct real solutions. If it is equal to 0, there will be one real solution (also known as a repeated root). If the discriminant is less than 0, there will be two complex solutions.
Since our discriminant is 56 which is greater than 0, we can conclude that there are two real solutions for our quadratic equation x² - 14 = 0.