Solve x(x-7)+7x-x^2/2x^2+9=0

$$\frac { x ( x - 7 ) + 7 x - x ^ { 2 } } { 2 x ^ { 2 } + 9 } = 0$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Multiply both sides of the equation by 2x^{2}+9.

$$x\left(x-7\right)+7x-x^{2}=0$$

Use the distributive property to multiply x by x-7.

$$x^{2}-7x+7x-x^{2}=0$$

Combine -7x and 7x to get 0.

$$x^{2}-x^{2}=0$$

Combine x^{2} and -x^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Solve for x (complex solution)

$$x\in \mathrm{C}\setminus -\frac{3\sqrt{2}i}{2},\frac{3\sqrt{2}i}{2}$$