Using factorization method solve the quadratic equation:
-60 -14x^2 + 82x
To solve the quadratic equation -14x^2 + 82x - 60 = 0 using factoring, we will try to find two binomials that when multiplied together, equal the quadratic equation.
First, let's group the terms:
(-14x^2 + 82x) - 60 = 0
Now, let's factor out the greatest common factor from the first two terms, which is 2x:
2x(-7x + 41) - 60 = 0
Next, let's factor out the greatest common factor from the last two terms, which is -20:
2x(-7x + 41) - 20(3) = 0
Now, we can rearrange the equation:
2x(-7x + 41) - 20(3) = 0
2x(-7x + 41) - 60 = 0
Now, we have a difference of squares:
(2x - 20)(-7x + 41) = 0
To find the values of x, we can set each binomial equal to zero and solve for x:
2x - 20 = 0 or -7x + 41 = 0
First equation:
2x = 20
x = 20/2
x = 10
Second equation:
-7x = -41
x = (-41)/(-7)
x ≈ 5.857
Therefore, the solutions to the quadratic equation -14x^2 + 82x - 60 = 0 are x = 10 and x ≈ 5.857.