find the x -intercept: $$ y=x^{2}-4 x-5 $$

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To find the x-intercept of the given quadratic equation $$ y = x^{2} - 4x - 5 $$, we need to set $$ y = 0 $$ and solve for $$ x $$.

Setting $$ y = 0 $$, we have:
$$ 0 = x^{2} - 4x - 5 $$

Now, we can solve this quadratic equation to find the x-intercept(s).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$0=x^{2}-4x-5$$
- step1: Swap the sides:
  $$x^{2}-4x-5=0$$
- step2: Factor the expression:
  $$\left(x-5\right)\left(x+1\right)=0$$
- step3: Separate into possible cases:
  $$\begin{align}&x-5=0\&x+1=0\end{align}$$
- step4: Solve the equation:
  $$\begin{align}&x=5\&x=-1\end{align}$$
- step5: Rewrite:
  $$x_{1}=-1,x_{2}=5$$
The x-intercept(s) of the quadratic equation $$ y = x^{2} - 4x - 5 $$ are $$ x = -1 $$ and $$ x = 5 $$.
The x-intercepts are $$ x = -1 $$ and $$ x = 5 $$.

find the x -intercept:

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