Find the real or imaginary solutions of the equation by factoring.

x^4-5x^2=-4

1 answer

To solve the equation x^4 - 5x^2 = -4 by factoring, we can rewrite it as x^4 - 5x^2 + 4 = 0.

Let's factor the left side of the equation:

(x^2 - 4)(x^2 - 1) = 0

Now we can set each factor equal to zero:

x^2 - 4 = 0 or x^2 - 1 = 0

For the first factor, we have:

(x - 2)(x + 2) = 0

Setting each factor equal to zero, we get:

x - 2 = 0 or x + 2 = 0

Solving for x in each equation, we find:

x = 2 or x = -2

For the second factor, we have:

(x - 1)(x + 1) = 0

Setting each factor equal to zero, we get:

x - 1 = 0 or x + 1 = 0

Solving for x in each equation, we find:

x = 1 or x = -1

Therefore, the solutions to the equation x^4 - 5x^2 = -4 are x = 2, x = -2, x = 1, and x = -1.