Solve x^2-bx+9=(x-3)^2

$$x ^ { 2 } - b x + 9 = ( x - 3 ) ^ { 2 }$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=6\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}-bx+9=x^{2}-6x+9$$

Subtract x^{2} from both sides.

$$-bx+9=x^{2}-6x+9-x^{2}$$

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

$$-bx+9=-6x+9$$

Subtract 9 from both sides.

$$-bx=-6x+9-9$$

Subtract 9 from 9 to get 0.

$$-bx=-6x$$

The equation is in standard form.

$$\left(-x\right)b=-6x$$

Divide both sides by -x.

$$\frac{\left(-x\right)b}{-x}=-\frac{6x}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$b=-\frac{6x}{-x}$$

Divide -6x by -x.

$$b=6$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&b=6\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}-bx+9=x^{2}-6x+9$$

Subtract x^{2} from both sides.

$$x^{2}-bx+9-x^{2}=-6x+9$$

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

$$-bx+9=-6x+9$$

Add 6x to both sides.

$$-bx+9+6x=9$$

Subtract 9 from both sides.

$$-bx+6x=9-9$$

Subtract 9 from 9 to get 0.

$$-bx+6x=0$$

Combine all terms containing x.

$$\left(-b+6\right)x=0$$

The equation is in standard form.

$$\left(6-b\right)x=0$$

Divide 0 by 6-b.

$$x=0$$

Solve for b

$$\left\{\begin{matrix}\\b=6\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}-bx+9=x^{2}-6x+9$$

Subtract x^{2} from both sides.

$$-bx+9=x^{2}-6x+9-x^{2}$$

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

$$-bx+9=-6x+9$$

Subtract 9 from both sides.

$$-bx=-6x+9-9$$

Subtract 9 from 9 to get 0.

$$-bx=-6x$$

The equation is in standard form.

$$\left(-x\right)b=-6x$$

Divide both sides by -x.

$$\frac{\left(-x\right)b}{-x}=-\frac{6x}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$b=-\frac{6x}{-x}$$

Divide -6x by -x.

$$b=6$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&b=6\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}-bx+9=x^{2}-6x+9$$

Subtract x^{2} from both sides.

$$x^{2}-bx+9-x^{2}=-6x+9$$

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

$$-bx+9=-6x+9$$

Add 6x to both sides.

$$-bx+9+6x=9$$

Subtract 9 from both sides.

$$-bx+6x=9-9$$

Subtract 9 from 9 to get 0.

$$-bx+6x=0$$

Combine all terms containing x.

$$\left(-b+6\right)x=0$$

The equation is in standard form.

$$\left(6-b\right)x=0$$

Divide 0 by 6-b.

$$x=0$$