Question

Determine whether the given values of variable is a solution of the quadratic equation or not. $x^2+14x+13=0;x=-1,x=-13$

Answer 1

The given quadratic equation is $x^2+14x+13=0$.

Substitute $x=-1$ in the equation $x^2+14x+13=0$ as follows:

$x^2+14x+13=0\Rightarrow (-1{)}^2+(14\times (-1))+13=0\Rightarrow 1-14+13=0\Rightarrow 14-14=0\Rightarrow 0=0$

which is true.

Therefore, $x=-1$ is the solution of the given quadratic equation.

Now, substitute $x=-13$ in the equation $x^2+14x+13=0$ as follows:

$x^2+14x+13=0\Rightarrow (-13{)}^2+(14\times (-13))+13=0\Rightarrow 169-182+13=0\Rightarrow 182-182=0\Rightarrow 0=0$

which is true.

Therefore, $x=-13$ is the solution of the given quadratic equation.

Hence, $x=-1$ and $x=-13$ are the solution of the quadratic equation $x^2+14x+13=0$.