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1) Solve

x2−4x−5=0 and enter solutions below.

2) Push the "Graph It" Button to see a graph of
y=x2−4x−5

Enter Solution 1:

1 answer

To solve the quadratic equation \(x^2 - 4x - 5 = 0\), we can factor it or use the quadratic formula.

First, let's try to factor it. We need two numbers that multiply to \(-5\) (the constant term) and add to \(-4\) (the coefficient of \(x\)). The numbers \(-5\) and \(1\) work since:

\[ -5 \times 1 = -5 \quad \text{and} \quad -5 + 1 = -4 \]

So we can factor the equation as:

\[ (x - 5)(x + 1) = 0 \]

Setting each factor to zero gives us the solutions:

  1. \(x - 5 = 0 \Rightarrow x = 5\)
  2. \(x + 1 = 0 \Rightarrow x = -1\)

Thus, the solutions to the equation \(x^2 - 4x - 5 = 0\) are:

  • Solution 1: \(5\)
  • Solution 2: \(-1\)

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