What are the solutions of the equation x^4 + 95x^2-500=0? Use factoring to solve

x = ± sqrt (5)

x = ±10i

Step-by-step explanation:

x^4 + 95x^2-500=0

What two numbers multiply to - 500 and add to 95

-5 * 100 = - 500

-5 + 100 = 95

(x^2 - 5) (x^2 + 100) = 0

Using the zero product property

x^2 - 5 = 0 x^2 + 100 = 0

x^2 - 5+5 = 0 x^2 + 100-100 = 0-100

x^2 = 5 x^2 = - 100

Take the square root of each side

x = ± sqrt (5) x = imaginary numbers

x = ±10i

x^4+100x^2-5x^2-500=0

x^2 (x^2+100) - 5 (x^2+100) = 0

(x^2+100) (x^2-5) = 0

from first expression

x^2+100=0

x^2=-100

x = root under - 100

Therefore x=-10

from next expression

x^2-5=0

x^2=5

Or x=2.23