Solve y=(6+x)(17-2x/2)

$$y = ( 6 + x ) ( \frac { 17 - 2 x } { 2 } )$$

Solve for y

$$y=-\frac{\left(2x-17\right)\left(x+6\right)}{2}$$

Solution Steps

Express \left(6+x\right)\times \frac{17-2x}{2} as a single fraction.

$$y=\frac{\left(6+x\right)\left(17-2x\right)}{2}$$

Use the distributive property to multiply 6+x by 17-2x and combine like terms.

$$y=\frac{102+5x-2x^{2}}{2}$$

Divide each term of 102+5x-2x^{2} by 2 to get 51+\frac{5}{2}x-x^{2}.

$$y=51+\frac{5}{2}x-x^{2}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{841-16y}+5}{4}$$

$$x=\frac{\sqrt{841-16y}+5}{4}$$

Solve for x

$$x=\frac{-\sqrt{841-16y}+5}{4}$$

$$x=\frac{\sqrt{841-16y}+5}{4}\text{, }y\leq \frac{841}{16}$$