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.
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.
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