Solve (m+1)x^2-8x+2=0

$$( m + 1 ) x ^ { 2 } - 8 x + 2 = 0$$

Solve for m

$$m=-1+\frac{8}{x}-\frac{2}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply m+1 by x^{2}.

$$mx^{2}+x^{2}-8x+2=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$mx^{2}-8x+2=-x^{2}$$

Add 8x to both sides.

$$mx^{2}+2=-x^{2}+8x$$

Subtract 2 from both sides.

$$mx^{2}=-x^{2}+8x-2$$

The equation is in standard form.

$$x^{2}m=-x^{2}+8x-2$$

Divide both sides by x^{2}.

$$\frac{x^{2}m}{x^{2}}=\frac{-x^{2}+8x-2}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$m=\frac{-x^{2}+8x-2}{x^{2}}$$

Divide -x^{2}+8x-2 by x^{2}.

$$m=-1+\frac{8x-2}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{2\left(7-m\right)}+4}{m+1}\text{; }x=\frac{-\sqrt{2\left(7-m\right)}+4}{m+1}\text{, }&m\neq -1\\x=\frac{1}{4}\text{, }&m=-1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{2\left(7-m\right)}+4}{m+1}\text{; }x=\frac{-\sqrt{2\left(7-m\right)}+4}{m+1}\text{, }&m\neq -1\text{ and }m\leq 7\\x=\frac{1}{4}\text{, }&m=-1\end{matrix}\right.$$