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x\left(x+2\right)+0\times 6=x^{2}+\frac{1}{5}
Multiply x and x to get x^{2}.
x^{2}+2x+0\times 6=x^{2}+\frac{1}{5}
Use the distributive property to multiply x by x+2.
x^{2}+2x+0=x^{2}+\frac{1}{5}
Multiply 0 and 6 to get 0.
x^{2}+2x=x^{2}+\frac{1}{5}
Anything plus zero gives itself.
x^{2}+2x-x^{2}=\frac{1}{5}
Subtract x^{2} from both sides.
2x=\frac{1}{5}
Combine x^{2} and -x^{2} to get 0.
x=\frac{\frac{1}{5}}{2}
Divide both sides by 2.
x=\frac{1}{5\times 2}
Express \frac{\frac{1}{5}}{2} as a single fraction.
x=\frac{1}{10}
Multiply 5 and 2 to get 10.