Question

10-9(с-2/3)+7/с-16=2с​

Answer 1

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)