- 35x2 = 40x
Solve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary.
To solve the quadratic equation 35x^2 = 40x by factoring, we would begin by subtracting 40x from both sides to bring all terms to one side of the equation:
35x^2 - 40x = 0
Next, we look for a common factor in both terms. In this case, the greatest common factor is 5x:
5x(7x - 8) = 0
Now, we can set each factor equal to zero and solve for x:
5x = 0 or 7x - 8 = 0
Solving the first equation, we get:
x = 0
Now, solving the second equation for x:
7x - 8 = 0
7x = 8
x = 8/7
Therefore, the solutions to the quadratic equation 35x^2 = 40x are x = 0 and x = 8/7.