Solve y=-2x^2/25+2x/5

$$y = - \frac { 2 x ^ { 2 } } { 25 } + \frac { 2 x } { 5 }$$

Solve for y

$$y=\frac{2x\left(5-x\right)}{25}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 5 is 25. Multiply \frac{2x}{5} times \frac{5}{5}.

$$y=-\frac{2x^{2}}{25}+\frac{5\times 2x}{25}$$

Since -\frac{2x^{2}}{25} and \frac{5\times 2x}{25} have the same denominator, add them by adding their numerators.

$$y=\frac{-2x^{2}+5\times 2x}{25}$$

Do the multiplications in -2x^{2}+5\times 2x.

$$y=\frac{-2x^{2}+10x}{25}$$

Divide each term of -2x^{2}+10x by 25 to get -\frac{2}{25}x^{2}+\frac{2}{5}x.

$$y=-\frac{2}{25}x^{2}+\frac{2}{5}x$$

Solve for x (complex solution)

$$x=\frac{5\sqrt{1-2y}+5}{2}$$

$$x=\frac{-5\sqrt{1-2y}+5}{2}$$

Solve for x

$$x=\frac{5\sqrt{1-2y}+5}{2}$$

$$x=\frac{-5\sqrt{1-2y}+5}{2}\text{, }y\leq \frac{1}{2}$$