Consider the following quadratic equation:
64x^2=25
Step 2 of 2 : Solve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary.
To solve the quadratic equation 64x^2 = 25 by factoring, we can rearrange the equation to have one side equal to zero:
64x^2 - 25 = 0
This equation is in the form of a difference of squares, where (8x)^2 - 5^2 = (8x + 5)(8x - 5).
Therefore, we have:
(8x + 5)(8x - 5) = 0
Now, set each factor equal to zero and solve for x:
8x + 5 = 0
8x = -5
x = -5/8
and
8x - 5 = 0
8x = 5
x = 5/8
So, the solutions to the quadratic equation 64x^2 = 25 by factoring are x = -5/8 and x = 5/8.