Use factoring to solve 5^4-8x^2=0

Not sure where to begin I got
x^2(5x^2)-8=0

No, what you got was

x^2(5x^2-8) = 0

so, x=0 or

5x^2-8 = 0
x^2 = 8/5
. . .

maybe you mean

5^4 - (8x)^2 = 0 ??????
that would be
25^2 - (8x)^2 =0
(25 - 8x)(25+8x) = 0
8x = 25
or
8x = -25

As usual, there are several ways a garbled posting might be interpreted. Damon's way has the advantage of a rational solution. Mine and others, such as

5^4 - (8)x^2

have square roots.

To solve the equation 5^4 - 8x^2 = 0 using factoring, we need to factor out a common term from the expression.

Let's factor out x^2 from both terms:

x^2 * (5^4/x^2) - 8 = 0

Now we simplify the equation:

(5^4/x^2) - 8 = 0

To continue simplifying, we can rewrite 5^4 as 625:

625/x^2 - 8 = 0

Now, let's multiply the entire equation by x^2 to eliminate the fraction:

x^2 * (625/x^2) - x^2 * 8 = 0

This simplifies to:

625 - 8x^2 = 0

Now our equation is simplified and we can proceed to solve it. Let's rearrange the terms:

-8x^2 + 625 = 0

To solve this equation, we can use factoring by grouping or by using the quadratic formula. However, in this case, it is easier to use factoring by noticing that 625 is a perfect square. It can be written as 25^2.

-8x^2 + 25^2 = 0

Now we have a difference of squares:

(-8x + 25)(8x + 25) = 0

Setting each factor equal to zero gives us two possible solutions:

-8x + 25 = 0 or 8x + 25 = 0

Solving each equation for x:

-8x = -25 or 8x = -25

x = -25/-8 or x = -25/8

x = 25/8 or x = -25/8

So, the solutions to the equation 5^4 - 8x^2 = 0 are x = 25/8 and x = -25/8.