Solve x^2-ax+7a-16=0

$$x ^ { 2 } - a x + 7 a - 16 = 0$$

Solve for a

$$a=-\frac{x^{2}-16}{7-x}$$

$$x\neq 7$$

Steps for Solving Linear Equation

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

$$-ax+7a-16=-x^{2}$$

Add 16 to both sides.

$$-ax+7a=-x^{2}+16$$

Combine all terms containing a.

$$\left(-x+7\right)a=-x^{2}+16$$

The equation is in standard form.

$$\left(7-x\right)a=16-x^{2}$$

Divide both sides by -x+7.

$$\frac{\left(7-x\right)a}{7-x}=\frac{16-x^{2}}{7-x}$$

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

$$a=\frac{16-x^{2}}{7-x}$$

Divide -x^{2}+16 by -x+7.

$$a=\frac{\left(4-x\right)\left(x+4\right)}{7-x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{a^{2}-28a+64}+a}{2}$$

$$x=\frac{-\sqrt{a^{2}-28a+64}+a}{2}$$

Solve for x

$$x=\frac{\sqrt{a^{2}-28a+64}+a}{2}$$

$$x=\frac{-\sqrt{a^{2}-28a+64}+a}{2}\text{, }a\geq 2\sqrt{33}+14\text{ or }a\leq 14-2\sqrt{33}$$