Solve (7x-a)^2=49x^2-bx+9

$$( 7 x - a ) ^ { 2 } = 49 x ^ { 2 } - b x + 9$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{14ax-a^{2}+9}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&\left(a=-3\text{ or }a=3\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(7x-a\right)^{2}.

$$49x^{2}-14xa+a^{2}=49x^{2}-bx+9$$

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

$$49x^{2}-bx+9=49x^{2}-14xa+a^{2}$$

Subtract 49x^{2} from both sides.

$$-bx+9=49x^{2}-14xa+a^{2}-49x^{2}$$

Combine 49x^{2} and -49x^{2} to get 0.

$$-bx+9=-14xa+a^{2}$$

Subtract 9 from both sides.

$$-bx=-14xa+a^{2}-9$$

The equation is in standard form.

$$\left(-x\right)b=-14ax+a^{2}-9$$

Divide both sides by -x.

$$\frac{\left(-x\right)b}{-x}=\frac{-14ax+a^{2}-9}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$b=\frac{-14ax+a^{2}-9}{-x}$$

Divide -14xa+a^{2}-9 by -x.

$$b=-\frac{-14ax+a^{2}-9}{x}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{14ax-a^{2}+9}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&x=0\text{ and }|a|=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(7x-a\right)^{2}.

$$49x^{2}-14xa+a^{2}=49x^{2}-bx+9$$

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

$$49x^{2}-bx+9=49x^{2}-14xa+a^{2}$$

Subtract 49x^{2} from both sides.

$$-bx+9=49x^{2}-14xa+a^{2}-49x^{2}$$

Combine 49x^{2} and -49x^{2} to get 0.

$$-bx+9=-14xa+a^{2}$$

Subtract 9 from both sides.

$$-bx=-14xa+a^{2}-9$$

The equation is in standard form.

$$\left(-x\right)b=-14ax+a^{2}-9$$

Divide both sides by -x.

$$\frac{\left(-x\right)b}{-x}=\frac{-14ax+a^{2}-9}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$b=\frac{-14ax+a^{2}-9}{-x}$$

Divide -14xa+a^{2}-9 by -x.

$$b=-\frac{-14ax+a^{2}-9}{x}$$

Solve for a (complex solution)

$$a=\sqrt{49x^{2}-bx+9}+7x$$

$$a=-\sqrt{49x^{2}-bx+9}+7x$$