Solve y=(20-14-x)(20+2x)+(18-14+x)(40-2x)

$$y=(20-14-x)(20+2x)+(18-14+x)(40-2x)$$

Solve for y

$$y=280+24x-4x^{2}$$

Solution Steps

Subtract 14 from 20 to get 6.

$$y=\left(6-x\right)\left(20+2x\right)+\left(18-14+x\right)\left(40-2x\right)$$

Use the distributive property to multiply 6-x by 20+2x and combine like terms.

$$y=120-8x-2x^{2}+\left(18-14+x\right)\left(40-2x\right)$$

Subtract 14 from 18 to get 4.

$$y=120-8x-2x^{2}+\left(4+x\right)\left(40-2x\right)$$

Use the distributive property to multiply 4+x by 40-2x and combine like terms.

$$y=120-8x-2x^{2}+160+32x-2x^{2}$$

Add 120 and 160 to get 280.

$$y=280-8x-2x^{2}+32x-2x^{2}$$

Combine -8x and 32x to get 24x.

$$y=280+24x-2x^{2}-2x^{2}$$

Combine -2x^{2} and -2x^{2} to get -4x^{2}.

$$y=280+24x-4x^{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{316-y}}{2}+3$$

$$x=-\frac{\sqrt{316-y}}{2}+3$$

Solve for x

$$x=\frac{\sqrt{316-y}}{2}+3$$

$$x=-\frac{\sqrt{316-y}}{2}+3\text{, }y\leq 316$$