Consider the following quadratic equation:
7x^2=15x−2
Step 2 of 2 : Solve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary.
To solve the quadratic equation by factoring, we need to rewrite the equation in the form of ax^2 + bx + c = 0.
7x^2 - 15x + 2 = 0
To factor this equation, we need to find two numbers whose product is ac (7 * 2 = 14) and whose sum is b (-15).
The two numbers that satisfy this condition are -14 and -1.
Therefore, we can rewrite the equation as:
7x^2 - 14x - x + 2 = 0
Then, we can group the terms and factor by grouping:
(7x^2 - 14x) + (-x + 2) = 0
7x(x - 2) - 1(x - 2) = 0
(7x - 1)(x - 2) = 0
Now, we can set each factor equal to zero and solve for x:
7x - 1 = 0 or x - 2 = 0
Solving these equations, we get:
7x = 1 or x = 2
x = 1/7 or x = 2
Therefore, the solutions to the quadratic equation are x = 1/7 and x = 2.