x^4- 3x² - 4 = 0

To solve the equation \( x^4 - 3x^2 - 4 = 0 \), we can use substitution. Let \( y = x^2 \). Then, the equation becomes:

\[ y^2 - 3y - 4 = 0 \]

Next, we can factor this quadratic equation. We need to find two numbers that multiply to \(-4\) and add to \(-3\). These numbers are \(-4\) and \(1\). Thus, we can factor the equation as follows:

\[ (y - 4)(y + 1) = 0 \]

Setting each factor equal to zero gives us:

1. \( y - 4 = 0 \) \(\Rightarrow y = 4\)
2. \( y + 1 = 0 \) \(\Rightarrow y = -1\)

Now, recalling that \( y = x^2 \), we substitute back:

1. For \( y = 4 \): \[ x^2 = 4 \quad \Rightarrow \quad x = \pm 2 \]

2. For \( y = -1 \): \[ x^2 = -1 \quad \Rightarrow \quad x = \pm i \]

So, the complete solution for the original equation \( x^4 - 3x^2 - 4 = 0 \) is:

\[ x = 2, \quad x = -2, \quad x = i, \quad x = -i \]

Thus, the solutions are \( x = 2, -2, i, -i \).