solve the following equation by grouping. X^2 + 10x + 21 = 0
To solve the given equation by grouping, we need to find two numbers whose sum is 10 and whose product is 21.
Let's try to factorize the equation:
(x + ?)(x + ?) = 0
We know that the coefficient of x^2 is 1, so the factors should look like:
(x + ?)(x + ?) = 0
To find the factors, we look for two numbers whose sum is 10 and whose product is 21.
The numbers 7 and 3 satisfy these conditions because 7 + 3 = 10 and 7 * 3 = 21.
Therefore, the equation can be factored as:
(x + 7)(x + 3) = 0
So, x + 7 = 0 or x + 3 = 0.
From x + 7 = 0, we get:
x = -7
From x + 3 = 0, we get:
x = -3
Hence, the solutions to the equation x^2 + 10x + 21 = 0 are x = -7 and x = -3.