Question

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

Answer 1

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

Step-by-step explanation:

Given equation:

                   $x^{2} + 10 x + 21 = 0$

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

                $x^{2} + 7 x + 3 x + 21 = 0$

                $x^{2} + 10 x + 21 = 0$ (so values obtained from factor method are correct)

Or, can use quadratic formula, for $a x^{2} + b x + c=0$, the solutions are given by:

                      $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

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

                     $x=\frac{-10 \pm \sqrt{10^{2}-(4 \times 1 \times 21)}}{2(1)}=\frac{-10 \pm \sqrt{100-84}}{2}$

                     $x=\frac{-10 \pm \sqrt{16}}{2}=\frac{-10 \pm 4}{2}$

So,

When  $x=\frac{-10+4}{2}=\frac{-6}{2}=-3$

When $x=\frac{-10-4}{2}=\frac{-14}{2}=-7$

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