Using factorisation method solve:
Y^2 + 114 + 237 = 0
To solve the equation Y^2 + 114 + 237 = 0 using the factoring method, we need to find two numbers whose product is equal to the product of the quadratic term coefficient (1) and the constant term (237), and whose sum is equal to the linear term coefficient (114).
Let's look for two numbers whose product is 237. The prime factorization of 237 is 3 * 79.
Next, we need to find two numbers whose product is 237 and whose sum is 114. Based on the prime factorization, we can see that the numbers are 3 and 79 since 3 + 79 = 82 and 3 * 79 = 237.
Now we can rewrite the equation as:
(Y + 3)(Y + 79) = 0
Setting each factor to zero, we have:
Y + 3 = 0 or Y + 79 = 0
Solving for Y, we get:
Y = -3 or Y = -79
Therefore, the solutions to the equation Y^2 + 114 + 237 = 0 are Y = -3 and Y = -79.