Solve c=x^2+2left(2x+3right)-3left(-2+xright)

$$c = { x }^{ 2 } +2 \left( 2x+3 \right) -3 \left( -2+x \right)$$

Solve for c

$$c=x^{2}+x+12$$

Solution Steps

Use the distributive property to multiply 2 by 2x+3.

$$c=x^{2}+4x+6-3\left(-2+x\right)$$

Use the distributive property to multiply -3 by -2+x.

$$c=x^{2}+4x+6+6-3x$$

Add 6 and 6 to get 12.

$$c=x^{2}+4x+12-3x$$

Combine 4x and -3x to get x.

$$c=x^{2}+x+12$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{4c-47}-1}{2}$$

$$x=\frac{\sqrt{4c-47}-1}{2}$$

Solve for x

$$x=\frac{-\sqrt{4c-47}-1}{2}$$

$$x=\frac{\sqrt{4c-47}-1}{2}\text{, }c\geq \frac{47}{4}$$