Consider the following quadratic equation:
25x^2=49
Step 2 of 2 : Solve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary.
To solve the equation 25x^2 = 49 by factoring, we can rewrite it as:
25x^2 - 49 = 0
Now, we can see that this equation is a difference of squares since 25x^2 is a perfect square (5x)^2 and 49 is a perfect square (7)^2. Applying the formula for the difference of squares, we have:
(5x + 7)(5x - 7) = 0
Setting each factor equal to zero, we have:
5x + 7 = 0 or 5x - 7 = 0
For the first equation, subtracting 7 from both sides, we get:
5x = -7
Dividing both sides by 5, we have:
x = -7/5
For the second equation, adding 7 to both sides, we get:
5x = 7
Dividing both sides by 5, we have:
x = 7/5
Therefore, the solutions to the quadratic equation 25x^2 = 49 by factoring are x = -7/5 and x = 7/5.