Solve S=2*(-1/2c^2+5/2c-2-(1/2c-2))

$$S = 2 \times (- \frac{ 1 }{ 2 } { c }^{ 2 } + \frac{ 5 }{ 2 } c-2-( \frac{ 1 }{ 2 } c-2))$$

Solve for S

$$S=-c\left(c-4\right)$$

Solution Steps

To find the opposite of \frac{1}{2}c-2, find the opposite of each term.

$$S=2\left(-\frac{1}{2}c^{2}+\frac{5}{2}c-2-\frac{1}{2}c+2\right)$$

Combine \frac{5}{2}c and -\frac{1}{2}c to get 2c.

$$S=2\left(-\frac{1}{2}c^{2}+2c-2+2\right)$$

Add -2 and 2 to get 0.

$$S=2\left(-\frac{1}{2}c^{2}+2c\right)$$

Use the distributive property to multiply 2 by -\frac{1}{2}c^{2}+2c.

$$S=-c^{2}+4c$$

Solve for c (complex solution)

$$c=-\sqrt{4-S}+2$$

$$c=\sqrt{4-S}+2$$

Solve for c

$$c=-\sqrt{4-S}+2$$

$$c=\sqrt{4-S}+2\text{, }S\leq 4$$