Solve A=x(2+x)+5(8-3x

$$A = x ( 2 + x ) + 5 ( 8 - 3 x$$

Solve for A

$$A=\left(x-8\right)\left(x-5\right)$$

Solution Steps

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

$$A=2x+x^{2}+5\left(8-3x\right)$$

Use the distributive property to multiply 5 by 8-3x.

$$A=2x+x^{2}+40-15x$$

Combine 2x and -15x to get -13x.

$$A=-13x+x^{2}+40$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{4A+9}+13}{2}$$

$$x=\frac{\sqrt{4A+9}+13}{2}$$

Solve for x

$$x=\frac{-\sqrt{4A+9}+13}{2}$$

$$x=\frac{\sqrt{4A+9}+13}{2}\text{, }A\geq -\frac{9}{4}$$