Ответы
To solve this equation, we will start by simplifying the expression on the left side:
10 - 9(c - 2/3) + 7/c - 16 = 2c
Multiplying through by the LCD (c), we have:
10c - 9c(c - 2/3) + 7 - 16c = 2c^2
Now, distribute -9c to c and -9 to -2/3:
10c - 9c^2 + 6/3 + 7 - 16c = 2c^2
Simplify the constants:
10c - 9c^2 + 2 + 7 - 16c = 2c^2
Combining like terms:
10c - 16c - 9c^2 + 2 + 7 = 2c^2
Combine constants:
10c - 16c - 9c^2 + 9 = 2c^2
Rearrange to get a quadratic equation:
0 = 2c^2 - 9c^2 + 10c - 16c + 9
Combine like terms:
0 = -7c^2 - 6c + 9
To solve this quadratic equation, we can either factor or use the quadratic formula. However, in this case, the equation does not factor nicely, so we will use the quadratic formula:
c = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = -7, b = -6, and c = 9. Plugging these values into the formula:
c = (6 ± √((-6)^2 - 4(-7)(9))) / (2(-7))
Simplifying the expression under the square root:
c = (6 ± √(36 + 252)) / (-14)
c = (6 ± √288) / (-14)
Simplifying the square root:
c = (6 ± √(16 * 18)) / (-14)
c = (6 ± 4√18) / (-14)
Now, we have two possible solutions for c:
c = (6 + 4√18) / (-14) or c = (6 - 4√18) / (-14)