Solve for a
a=25-bt
Solve for b
\left\{\begin{matrix}b=-\frac{a-25}{t}\text{, }&t\neq 0\\b\in \mathrm{R}\text{, }&a=25\text{ and }t=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=-\frac{a-25}{t}\text{, }&t\neq 0\\b\in \mathrm{C}\text{, }&a=25\text{ and }t=0\end{matrix}\right.
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\sqrt{a+bt}=5
Swap sides so that all variable terms are on the left hand side.
a+bt=25
Square both sides of the equation.
a+bt-bt=25-bt
Subtract bt from both sides of the equation.
a=25-bt
Subtracting bt from itself leaves 0.
\sqrt{a+bt}=5
Swap sides so that all variable terms are on the left hand side.
tb+a=25
Square both sides of the equation.
tb+a-a=25-a
Subtract a from both sides of the equation.
tb=25-a
Subtracting a from itself leaves 0.
\frac{tb}{t}=\frac{25-a}{t}
Divide both sides by t.
b=\frac{25-a}{t}
Dividing by t undoes the multiplication by t.
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