Solve C=-x(3x+1)+(-5)(9x-1)

$$C = - x ( 3 x + 1 ) + ( - 5 ) ( 9 x - 1 )$$

Solve for C

$$C=5-46x-3x^{2}$$

Solution Steps

Use the distributive property to multiply -x by 3x+1.

$$C=3\left(-x\right)x-x-5\left(9x-1\right)$$

Use the distributive property to multiply -5 by 9x-1.

$$C=3\left(-x\right)x-x-45x+5$$

Multiply x and x to get x^{2}.

$$C=3\left(-1\right)x^{2}-x-45x+5$$

Multiply 3 and -1 to get -3.

$$C=-3x^{2}-x-45x+5$$

Combine -x and -45x to get -46x.

$$C=-3x^{2}-46x+5$$

Solve for x (complex solution)

$$x=\frac{\sqrt{544-3C}-23}{3}$$

$$x=\frac{-\sqrt{544-3C}-23}{3}$$

Solve for x

$$x=\frac{\sqrt{544-3C}-23}{3}$$

$$x=\frac{-\sqrt{544-3C}-23}{3}\text{, }C\leq \frac{544}{3}$$