Solve D=5x+1-(x+4)(x-9)

$$D = 5 x + 1 - ( x + 4 ) ( x - 9 )$$

Solve for D

$$D=37+10x-x^{2}$$

Solution Steps

Use the distributive property to multiply x+4 by x-9 and combine like terms.

$$D=5x+1-\left(x^{2}-5x-36\right)$$

To find the opposite of x^{2}-5x-36, find the opposite of each term.

$$D=5x+1-x^{2}+5x+36$$

Combine 5x and 5x to get 10x.

$$D=10x+1-x^{2}+36$$

Add 1 and 36 to get 37.

$$D=10x+37-x^{2}$$

Solve for x (complex solution)

$$x=-\sqrt{62-D}+5$$

$$x=\sqrt{62-D}+5$$

Solve for x

$$x=-\sqrt{62-D}+5$$

$$x=\sqrt{62-D}+5\text{, }D\leq 62$$