Find the solution(s) for x in the equation below. x^2 + 10x + 21= 0

The solutions for ‘x’ in the given equation are – 3  and  - 7

Step-by-step explanation:

Given equation:

To find the ‘x’ value, try to factor, because in this case it works, it's fast. By using factor method, we get

                    (x + 3) (x + 7) = 0  (adding both value we get 10 and multiply as 21 as in equation and check with signs also while factoring)

                     x = - 3, -7

Verify above values by multiply both terms,

                     (x + 3) (x + 7) = 0

                (so values obtained from factor method are correct)

Or, can use quadratic formula, for , the solutions are given by:

In the given equation, a = 1, b = 10, c = 21, apply these in above formula

So,

When  

When

Hence, the values for ‘x’ are - 3 and - 7

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this