Solve the following quadratic equation by factoring. x2+11x+28=0

Question:- Solve the following quadratic equation by factoring. x2+11x+28=0

Answer: To solve this quadratic equation by factoring, we’ll follow these steps

First, let’s identify the coefficients: a = 1, b = 11, c = 28

Thus we have two numbers which, when they are multiplied, will produce ac and that is 1*28 =28 and adding two numbers will produce b as 11. These numbers are 7 and 4

We can rewrite the middle term using these numbers: x^2+7x+4x+28=0

Now we can factor by grouping: Again, it gets to simplify the equation to get ( 2x + 7) + (4x + 28) = 0

thus minimizing the expression gets x(x + 7) + 4(x + 7) = 0

In order to factor it the expression gets into (x + 7)(x + 4) = 0

Using the zero-product property, we can set each factor to zero

So, we get x = -7 or x = -4 (after substituting x + 7 = 0 or x + 4 = 0. )

As such, they are the solutions to the equation x² + 11x + 28 = 0; this means that the solutions are -7 and -4.