query: Solve for $x$ in the $80^\circ$-$80^\circ$-$20^\circ$ triangle
positive_passages.docid: 40919
positive_passages.text: Finding an angle within an 80-80-20 isosceles triangle
negative_passages.docid: 103993
negative_passages.text: Find all real solutions for $x$ in $2(2^x−1)x^2+(2^{x^2}−2)x=2^{x+1}−2$.
negative_passages.docid: 15753
negative_passages.text: Solve the following equation in positive integers $x$ and $y$
negative_passages.docid: 94965
negative_passages.text: Solve $x\equiv 1\pmod2$, $x\equiv 2\pmod3$, $x\equiv 3\pmod4$, $x\equiv 4\pmod5$, $x\equiv 5\pmod6$ and $x\equiv 0\pmod7$
negative_passages.docid: 82016
negative_passages.text: Given $p^2+q^2+r^2+1=s+\sqrt{p+q+r-s}$, solve for $s$
negative_passages.docid: 36438
negative_passages.text: How to solve infinite repeating exponents
negative_passages.docid: 142673
negative_passages.text: Evaluate $\tan^{2}(20^{\circ}) + \tan^{2}(40^{\circ}) + \tan^{2}(80^{\circ})$
negative_passages.docid: 15897
negative_passages.text: Solve a congruence $1978^{20}\equiv x\pmod{125}$
negative_passages.docid: 144765
negative_passages.text: Solving $\sqrt{x+5} = x - 1$
negative_passages.docid: 28502
negative_passages.text: How to solve $x^3=-1$?
negative_passages.docid: 121237
negative_passages.text: Solving $x - a \log(x)=b$
negative_passages.docid: 87066
negative_passages.text: How do I solve the following equation?
negative_passages.docid: 138078
negative_passages.text: Solve $2000x^6+100x^5+10x^3+x-2=0$
negative_passages.docid: 148570
negative_passages.text: Find the all possible real solutions of $x^y=y^x$
negative_passages.docid: 123867
negative_passages.text: Solve $(a + b\sin(x))\sin(x) = p$ for $x$
negative_passages.docid: 117697
negative_passages.text: How to solve 5x=0.01^x
negative_passages.docid: 24307
negative_passages.text: Is $x^x=y$ solvable for $x$?