Using quadratic equation, solve:
-60 -14x^2 + 82x
To solve this equation using the quadratic equation, we need to set the equation equal to zero:
-14x^2 + 82x - 60 = 0
Now we can use the quadratic formula, which is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = -14, b = 82, and c = -60. Plugging in these values into the quadratic formula, we have:
x = (-82 ± √(82^2 - 4(-14)(-60))) / (2(-14))
Simplifying further:
x = (-82 ± √(6724 - 3360)) / (-28)
x = (-82 ± √3364) / (-28)
Now, let's consider the two possibilities for x:
1. If we take the positive square root:
x = (-82 + √3364) / (-28)
x = (-82 + 58) / (-28)
x = (-24) / (-28)
x = 0.86
2. If we take the negative square root:
x = (-82 - √3364) / (-28)
x = (-82 - 58) / (-28)
x = (-140) / (-28)
x = 5
Therefore, the solutions to the quadratic equation -60 -14x^2 + 82x = 0 are x = 0.86 and x = 5.