Question

x^4-29x^2=100 solve and show all you work and steps

Answer 1

To solve the equation x^4 - 29x^2 = 100, we can rearrange the equation to set it equal to zero:

x^4 - 29x^2 - 100 = 0

Let's substitute u = x^2 to simplify the equation:

u^2 - 29u - 100 = 0

Now, we can factor this quadratic equation:

(u - 25)(u + 4) = 0

Setting each factor equal to zero, we have:

u - 25 = 0 or u + 4 = 0

Solving for u:

u = 25 or u = -4

Substituting back the value of u to x^2:

x^2 = 25 or x^2 = -4

For x^2 = 25, we can take the square root of both sides:

x = ±√25
x = ±5

For x^2 = -4, since the square of any real number cannot be negative, there are no real solutions for this case.

Therefore, the solutions to the equation x^4 - 29x^2 = 100 are x = 5 and x = -5.