How do you solve # 2x^4 = 16x^2#?

Question

Avery Alexander · Accepted Answer

Put both terms to one side of the equation and then factor.

#2x^4 - 16x^2 = 0# #2x^2(x^2 - 8) = 0# #x = 0 and +- sqrt(8)# Hopefully this helps!

Hazel Anglin · Answer

set the equation equal to zero and factor

You can either set the equation equal to zero and factor or you can proceed as follows: divide both sides by 2 divide both sides by x^2 then set the equation = 0

Avery Alexander · Answer

undefined To solve the equation 2x^4 = 16x^2, you first need to rearrange it to bring all terms to one side and set the equation equal to zero. Then, factor out common terms, if possible. Next, apply the zero-product property to find the values of x that make each factor equal to zero. Finally, solve for x.

Here's the step-by-step solution:
1. Rewrite the equation as 2x^4 - 16x^2 = 0.
2. Factor out the common term, which is 2x^2: 2x^2(x^2 - 8) = 0.
3. Apply the zero-product property: Set each factor equal to zero.
   - 2x^2 = 0 → x = 0
   - x^2 - 8 = 0
4. Solve x^2 - 8 = 0 for x:
   - Add 8 to both sides: x^2 = 8.
   - Take the square root of both sides: x = ±√8.
5. Simplify √8 to get the final solutions:
   - x = ±2√2.

Therefore, the solutions to the equation 2x^4 = 16x^2 are x = 0 and x = ±2√2.