Solve y=-((x-2)(x-5))+3

$$y=-((x-2)(x-5))+3$$

Solve for y

$$y=-\left(x-5\right)\left(x-2\right)+3$$

Solution Steps

Use the distributive property to multiply x-2 by x-5 and combine like terms.

$$y=-\left(x^{2}-7x+10\right)+3$$

To find the opposite of x^{2}-7x+10, find the opposite of each term.

$$y=-x^{2}+7x-10+3$$

Add -10 and 3 to get -7.

$$y=-x^{2}+7x-7$$

Solve for x (complex solution)

$$x=\frac{\sqrt{21-4y}+7}{2}$$

$$x=\frac{-\sqrt{21-4y}+7}{2}$$

Solve for x

$$x=\frac{\sqrt{21-4y}+7}{2}$$

$$x=\frac{-\sqrt{21-4y}+7}{2}\text{, }y\leq \frac{21}{4}$$