Verified answer

4x^2(x-10)(x+10) = 0 ----> x = 0, 10, -10

4x^(4)-400x^(2)=0 ( / means plus or minus and ~ means square root)

Factor out the GCF of 4x^(2) from each term in the polynomial.

4x^(2)(x^(2))+4x^(2)(-100)=0

Factor out the GCF of 4x^(2) from 4x^(4)-400x^(2).

4x^(2)(x^(2)-100)=0

The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).

4x^(2)(x-10)(x+10)=0

Set the single term factor on the left-hand side of the equation equal to 0.

4x^(2)=0

Divide each term in the equation by 4.

(4x^(2))/(4)=(0)/(4)

Simplify the left-hand side of the equation by canceling the common terms.

x^(2)=(0)/(4)

0 divided by any number or variable is 0.

x^(2)=0

Take the square root of both sides of the equation to eliminate the exponent on the left-hand side.

x=\~(0)

Pull all perfect square roots out from under the radical. In this case, remove the 0 because it is a perfect square.

x=\0

\0 is equal to 0.

x=0

Set each of the factors of the left-hand side of the equation equal to 0.

x-10=0

Since -10 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 10 to both sides.

x+10=0

Set each of the factors of the left-hand side of the equation equal to 0.

x+10=0

Since 10 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 10 from both sides.

x=-10

The complete solution is the set of the individual solutions.

x=0,10,-10

4x^4-400x^2=0

4x^2(x^2 - 100)= 0

(0/4x^2 = 0)

x/^2 -100 = 0

x^2 = 100

x = 10

8x^2(3x^2-50) = 0

8x^2=0 or 3x^2 = 50

x=0 or x^ = 50/3

x=0 or x = sqrt(50/3) or x= - sqrt(50/3)

what are they asking you to do? solve for x or just factor this equation?