Solve x^2-left(a-2bright)x-2ab=0

$${ x }^{ 2 } - \left( a-2b \right) x-2ab=0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=x\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=-2b\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a-2b by x.

$$x^{2}-\left(ax-2bx\right)-2ab=0$$

To find the opposite of ax-2bx, find the opposite of each term.

$$x^{2}-ax+2bx-2ab=0$$

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

$$-ax+2bx-2ab=-x^{2}$$

Subtract 2bx from both sides.

$$-ax-2ab=-x^{2}-2bx$$

Combine all terms containing a.

$$\left(-x-2b\right)a=-x^{2}-2bx$$

Divide both sides by -x-2b.

$$\frac{\left(-x-2b\right)a}{-x-2b}=-\frac{x\left(x+2b\right)}{-x-2b}$$

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

$$a=-\frac{x\left(x+2b\right)}{-x-2b}$$

Divide -x\left(x+2b\right) by -x-2b.

$$a=x$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=-\frac{x}{2}\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=a\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a-2b by x.

$$x^{2}-\left(ax-2bx\right)-2ab=0$$

To find the opposite of ax-2bx, find the opposite of each term.

$$x^{2}-ax+2bx-2ab=0$$

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

$$-ax+2bx-2ab=-x^{2}$$

Add ax to both sides.

$$2bx-2ab=-x^{2}+ax$$

Combine all terms containing b.

$$\left(2x-2a\right)b=-x^{2}+ax$$

The equation is in standard form.

$$\left(2x-2a\right)b=ax-x^{2}$$

Divide both sides by 2x-2a.

$$\frac{\left(2x-2a\right)b}{2x-2a}=\frac{x\left(a-x\right)}{2x-2a}$$

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

$$b=\frac{x\left(a-x\right)}{2x-2a}$$

Divide x\left(-x+a\right) by 2x-2a.

$$b=-\frac{x}{2}$$

Solve for a

$$\left\{\begin{matrix}\\a=x\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=-2b\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a-2b by x.

$$x^{2}-\left(ax-2bx\right)-2ab=0$$

To find the opposite of ax-2bx, find the opposite of each term.

$$x^{2}-ax+2bx-2ab=0$$

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

$$-ax+2bx-2ab=-x^{2}$$

Subtract 2bx from both sides.

$$-ax-2ab=-x^{2}-2bx$$

Combine all terms containing a.

$$\left(-x-2b\right)a=-x^{2}-2bx$$

Divide both sides by -x-2b.

$$\frac{\left(-x-2b\right)a}{-x-2b}=-\frac{x\left(x+2b\right)}{-x-2b}$$

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

$$a=-\frac{x\left(x+2b\right)}{-x-2b}$$

Divide -x\left(x+2b\right) by -x-2b.

$$a=x$$

Solve for b

$$\left\{\begin{matrix}\\b=-\frac{x}{2}\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=a\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a-2b by x.

$$x^{2}-\left(ax-2bx\right)-2ab=0$$

To find the opposite of ax-2bx, find the opposite of each term.

$$x^{2}-ax+2bx-2ab=0$$

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

$$-ax+2bx-2ab=-x^{2}$$

Add ax to both sides.

$$2bx-2ab=-x^{2}+ax$$

Combine all terms containing b.

$$\left(2x-2a\right)b=-x^{2}+ax$$

The equation is in standard form.

$$\left(2x-2a\right)b=ax-x^{2}$$

Divide both sides by 2x-2a.

$$\frac{\left(2x-2a\right)b}{2x-2a}=\frac{x\left(a-x\right)}{2x-2a}$$

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

$$b=\frac{x\left(a-x\right)}{2x-2a}$$

Divide x\left(-x+a\right) by 2x-2a.

$$b=-\frac{x}{2}$$