Question

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

Answer 1

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

Explanation:

Answer 2

x = ± sqrt(5)

x = ±10i

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