Solve for b (complex solution)
\left\{\begin{matrix}b=-\frac{cx-S}{x-c}\text{, }&x\neq c\\b\in \mathrm{C}\text{, }&S=x^{2}\text{ and }c=x\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-\frac{cx-S}{x-c}\text{, }&x\neq c\\b\in \mathrm{R}\text{, }&S=x^{2}\text{ and }c=x\end{matrix}\right.
Solve for S
S=bx+cx-bc
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bx-bc+cx=S
Swap sides so that all variable terms are on the left hand side.
bx-bc=S-cx
Subtract cx from both sides.
\left(x-c\right)b=S-cx
Combine all terms containing b.
\frac{\left(x-c\right)b}{x-c}=\frac{S-cx}{x-c}
Divide both sides by x-c.
b=\frac{S-cx}{x-c}
Dividing by x-c undoes the multiplication by x-c.
bx-bc+cx=S
Swap sides so that all variable terms are on the left hand side.
bx-bc=S-cx
Subtract cx from both sides.
\left(x-c\right)b=S-cx
Combine all terms containing b.
\frac{\left(x-c\right)b}{x-c}=\frac{S-cx}{x-c}
Divide both sides by x-c.
b=\frac{S-cx}{x-c}
Dividing by x-c undoes the multiplication by x-c.
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