Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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x^{2}+2x+3=x^{2}+2x+1+2
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+2x+3=x^{2}+2x+3
Add 1 and 2 to get 3.
x^{2}+2x+3-x^{2}=2x+3
Subtract x^{2} from both sides.
2x+3=2x+3
Combine x^{2} and -x^{2} to get 0.
2x+3-2x=3
Subtract 2x from both sides.
3=3
Combine 2x and -2x to get 0.
\text{true}
Compare 3 and 3.
x\in \mathrm{C}
This is true for any x.
x^{2}+2x+3=x^{2}+2x+1+2
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{2}+2x+3=x^{2}+2x+3
Add 1 and 2 to get 3.
x^{2}+2x+3-x^{2}=2x+3
Subtract x^{2} from both sides.
2x+3=2x+3
Combine x^{2} and -x^{2} to get 0.
2x+3-2x=3
Subtract 2x from both sides.
3=3
Combine 2x and -2x to get 0.
\text{true}
Compare 3 and 3.
x\in \mathrm{R}
This is true for any x.
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Limits
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