Solve for a (complex solution)
a\in \mathrm{C}
Solve for x (complex solution)
x\in \mathrm{C}
Solve for a
a\in \mathrm{R}
Solve for x
x\in \mathrm{R}
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x^{2}+2xa+a^{2}=x^{2}+2ax+a^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+a\right)^{2}.
x^{2}+2xa+a^{2}-2ax=x^{2}+a^{2}
Subtract 2ax from both sides.
x^{2}+a^{2}=x^{2}+a^{2}
Combine 2xa and -2ax to get 0.
x^{2}+a^{2}-a^{2}=x^{2}
Subtract a^{2} from both sides.
x^{2}=x^{2}
Combine a^{2} and -a^{2} to get 0.
\text{true}
Reorder the terms.
a\in \mathrm{C}
This is true for any a.
x^{2}+2xa+a^{2}=x^{2}+2ax+a^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(x+a\right)^{2}.
x^{2}+2xa+a^{2}-x^{2}=2ax+a^{2}
Subtract x^{2} from both sides.
2xa+a^{2}=2ax+a^{2}
Combine x^{2} and -x^{2} to get 0.
2xa+a^{2}-2ax=a^{2}
Subtract 2ax from both sides.
a^{2}=a^{2}
Combine 2xa and -2ax to get 0.
\text{true}
Reorder the terms.
x\in \mathrm{C}
This is true for any x.
x^{2}+2xa+a^{2}=x^{2}+2ax+a^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+a\right)^{2}.
x^{2}+2xa+a^{2}-2ax=x^{2}+a^{2}
Subtract 2ax from both sides.
x^{2}+a^{2}=x^{2}+a^{2}
Combine 2xa and -2ax to get 0.
x^{2}+a^{2}-a^{2}=x^{2}
Subtract a^{2} from both sides.
x^{2}=x^{2}
Combine a^{2} and -a^{2} to get 0.
\text{true}
Reorder the terms.
a\in \mathrm{R}
This is true for any a.
x^{2}+2xa+a^{2}=x^{2}+2ax+a^{2}
Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(x+a\right)^{2}.
x^{2}+2xa+a^{2}-x^{2}=2ax+a^{2}
Subtract x^{2} from both sides.
2xa+a^{2}=2ax+a^{2}
Combine x^{2} and -x^{2} to get 0.
2xa+a^{2}-2ax=a^{2}
Subtract 2ax from both sides.
a^{2}=a^{2}
Combine 2xa and -2ax to get 0.
\text{true}
Reorder the terms.
x\in \mathrm{R}
This is true for any x.
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}