Solve for a (complex solution)
\left\{\begin{matrix}\\a=\frac{x-1}{2}\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=-1\end{matrix}\right.
Solve for a
\left\{\begin{matrix}\\a=\frac{x-1}{2}\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=-1\end{matrix}\right.
Solve for x
x=-1
x=2a+1
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x^{2}-2ax-2a=1
Subtract 2a from both sides.
-2ax-2a=1-x^{2}
Subtract x^{2} from both sides.
\left(-2x-2\right)a=1-x^{2}
Combine all terms containing a.
\frac{\left(-2x-2\right)a}{-2x-2}=\frac{1-x^{2}}{-2x-2}
Divide both sides by -2x-2.
a=\frac{1-x^{2}}{-2x-2}
Dividing by -2x-2 undoes the multiplication by -2x-2.
a=\frac{x-1}{2}
Divide -x^{2}+1 by -2x-2.
x^{2}-2ax-2a=1
Subtract 2a from both sides.
-2ax-2a=1-x^{2}
Subtract x^{2} from both sides.
\left(-2x-2\right)a=1-x^{2}
Combine all terms containing a.
\frac{\left(-2x-2\right)a}{-2x-2}=\frac{1-x^{2}}{-2x-2}
Divide both sides by -2x-2.
a=\frac{1-x^{2}}{-2x-2}
Dividing by -2x-2 undoes the multiplication by -2x-2.
a=\frac{x-1}{2}
Divide -x^{2}+1 by -2x-2.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}