Solve for B (complex solution)
\left\{\begin{matrix}B=\frac{16\times \left(\frac{25x-1}{20x-1}\right)^{2}}{25S}\text{, }&x\neq \frac{1}{20}\text{ and }S\neq 0\\B\in \mathrm{C}\text{, }&S=0\text{ and }x=\frac{1}{25}\end{matrix}\right.
Solve for S (complex solution)
\left\{\begin{matrix}S=\frac{16\times \left(\frac{25x-1}{20x-1}\right)^{2}}{25B}\text{, }&x\neq \frac{1}{20}\text{ and }B\neq 0\\S\in \mathrm{C}\text{, }&B=0\text{ and }x=\frac{1}{25}\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=\frac{16\times \left(\frac{25x-1}{20x-1}\right)^{2}}{25S}\text{, }&x\neq \frac{1}{20}\text{ and }S\neq 0\\B\in \mathrm{R}\text{, }&S=0\text{ and }x=\frac{1}{25}\end{matrix}\right.
Solve for S
\left\{\begin{matrix}S=\frac{16\times \left(\frac{25x-1}{20x-1}\right)^{2}}{25B}\text{, }&x\neq \frac{1}{20}\text{ and }B\neq 0\\S\in \mathrm{R}\text{, }&B=0\text{ and }x=\frac{1}{25}\end{matrix}\right.
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Linear Equation
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B S = \frac { ( 0.04 - x ) ^ { 2 } } { ( 0.05 - x ) ^ { 2 } }
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BS=\frac{0.0016-0.08x+x^{2}}{\left(0.05-x\right)^{2}}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0.04-x\right)^{2}.
BS=\frac{0.0016-0.08x+x^{2}}{0.0025-0.1x+x^{2}}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0.05-x\right)^{2}.
SB=\frac{x^{2}-\frac{2x}{25}+0.0016}{x^{2}-\frac{x}{10}+0.0025}
The equation is in standard form.
\frac{SB}{S}=\frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}S}
Divide both sides by S.
B=\frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}S}
Dividing by S undoes the multiplication by S.
B=\frac{16\left(25x-1\right)^{2}}{25S\left(20x-1\right)^{2}}
Divide \frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}} by S.
BS=\frac{0.0016-0.08x+x^{2}}{\left(0.05-x\right)^{2}}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0.04-x\right)^{2}.
BS=\frac{0.0016-0.08x+x^{2}}{0.0025-0.1x+x^{2}}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0.05-x\right)^{2}.
BS=\frac{x^{2}-\frac{2x}{25}+0.0016}{x^{2}-\frac{x}{10}+0.0025}
The equation is in standard form.
\frac{BS}{B}=\frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}B}
Divide both sides by B.
S=\frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}B}
Dividing by B undoes the multiplication by B.
S=\frac{16\left(25x-1\right)^{2}}{25B\left(20x-1\right)^{2}}
Divide \frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}} by B.
BS=\frac{0.0016-0.08x+x^{2}}{\left(0.05-x\right)^{2}}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0.04-x\right)^{2}.
BS=\frac{0.0016-0.08x+x^{2}}{0.0025-0.1x+x^{2}}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0.05-x\right)^{2}.
SB=\frac{x^{2}-\frac{2x}{25}+0.0016}{x^{2}-\frac{x}{10}+0.0025}
The equation is in standard form.
\frac{SB}{S}=\frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}S}
Divide both sides by S.
B=\frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}S}
Dividing by S undoes the multiplication by S.
B=\frac{16\left(25x-1\right)^{2}}{25S\left(20x-1\right)^{2}}
Divide \frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}} by S.
BS=\frac{0.0016-0.08x+x^{2}}{\left(0.05-x\right)^{2}}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0.04-x\right)^{2}.
BS=\frac{0.0016-0.08x+x^{2}}{0.0025-0.1x+x^{2}}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0.05-x\right)^{2}.
BS=\frac{x^{2}-\frac{2x}{25}+0.0016}{x^{2}-\frac{x}{10}+0.0025}
The equation is in standard form.
\frac{BS}{B}=\frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}B}
Divide both sides by B.
S=\frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}B}
Dividing by B undoes the multiplication by B.
S=\frac{16\left(25x-1\right)^{2}}{25B\left(20x-1\right)^{2}}
Divide \frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}} by B.
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