Solve x^2=(x+7)*(c-2)

$$x ^ { 2 } = ( x + 7 ) \times ( c - 2 )$$

Solve for c

$$c=\frac{x^{2}+2x+14}{x+7}$$

$$x\neq -7$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+7 by c-2.

$$x^{2}=xc-2x+7c-14$$

Swap sides so that all variable terms are on the left hand side.

$$xc-2x+7c-14=x^{2}$$

Add 2x to both sides.

$$xc+7c-14=x^{2}+2x$$

Add 14 to both sides.

$$xc+7c=x^{2}+2x+14$$

Combine all terms containing c.

$$\left(x+7\right)c=x^{2}+2x+14$$

Divide both sides by x+7.

$$\frac{\left(x+7\right)c}{x+7}=\frac{x^{2}+2x+14}{x+7}$$

Dividing by x+7 undoes the multiplication by x+7.

$$c=\frac{x^{2}+2x+14}{x+7}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{\left(c-2\right)\left(c+26\right)}+c-2}{2}$$

$$x=\frac{-\sqrt{\left(c-2\right)\left(c+26\right)}+c-2}{2}$$

Solve for x

$$x=\frac{\sqrt{\left(c-2\right)\left(c+26\right)}+c-2}{2}$$

$$x=\frac{-\sqrt{\left(c-2\right)\left(c+26\right)}+c-2}{2}\text{, }c\leq -26\text{ or }c\geq 2$$