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.