Solve w=(x-10)(-x+40)

$$w = ( x - 10 ) ( - x + 40 )$$

Solve for w

$$w=-\left(x-40\right)\left(x-10\right)$$

Solution Steps

Use the distributive property to multiply x-10 by -x+40.

$$w=x\left(-x\right)+40x-10\left(-x\right)-400$$

Multiply -10 and -1 to get 10.

$$w=x\left(-x\right)+40x+10x-400$$

Combine 40x and 10x to get 50x.

$$w=x\left(-x\right)+50x-400$$

Multiply x and x to get x^{2}.

$$w=x^{2}\left(-1\right)+50x-400$$

Solve for x (complex solution)

$$x=\sqrt{225-w}+25$$

$$x=-\sqrt{225-w}+25$$

Solve for x

$$x=\sqrt{225-w}+25$$

$$x=-\sqrt{225-w}+25\text{, }w\leq 225$$