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

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

Solve for m

$$m=-\frac{x^{2}+4x-1}{2\left(x-1\right)}$$

$$x\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by m+2.

$$x^{2}+\left(2m+4\right)x-2m-1=0$$

Use the distributive property to multiply 2m+4 by x.

$$x^{2}+2mx+4x-2m-1=0$$

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

$$2mx+4x-2m-1=-x^{2}$$

Subtract 4x from both sides.

$$2mx-2m-1=-x^{2}-4x$$

Add 1 to both sides.

$$2mx-2m=-x^{2}-4x+1$$

Combine all terms containing m.

$$\left(2x-2\right)m=-x^{2}-4x+1$$

The equation is in standard form.

$$\left(2x-2\right)m=1-4x-x^{2}$$

Divide both sides by 2x-2.

$$\frac{\left(2x-2\right)m}{2x-2}=\frac{1-4x-x^{2}}{2x-2}$$

Dividing by 2x-2 undoes the multiplication by 2x-2.

$$m=\frac{1-4x-x^{2}}{2x-2}$$

Divide -x^{2}-4x+1 by 2x-2.

$$m=\frac{1-4x-x^{2}}{2\left(x-1\right)}$$

Solve for x (complex solution)

$$x=\sqrt{\left(m+1\right)\left(m+5\right)}-m-2$$

$$x=-\sqrt{\left(m+1\right)\left(m+5\right)}-m-2$$

Solve for x

$$x=\sqrt{\left(m+1\right)\left(m+5\right)}-m-2$$

$$x=-\sqrt{\left(m+1\right)\left(m+5\right)}-m-2\text{, }m\leq -5\text{ or }m\geq -1$$