query: Solving $(x^2+4x+3)^x+(2x+4)^x=(x^2+4x+5)^x$ with $x\in(-1,\infty)$
positive_passages.docid: 146753
positive_passages.text: Find $x$ such that $(x^2 + 4x + 3)^x + (2x + 4)^x = (x^2 + 4x + 5)^x$
negative_passages.docid: 76990
negative_passages.text: Find $\lim_{x \to - \infty} \left(\frac{4^{x+2}- 2\cdot3^{-x}}{4^{-x}+2\cdot3^{x+1}}\right)$
negative_passages.docid: 64448
negative_passages.text: Find a quadratic equation with root $x_1^2$ and $x_2^2$
negative_passages.docid: 8676
negative_passages.text: Is there any "superlogarithm" or something to solve $x^x$?
negative_passages.docid: 55197
negative_passages.text: Roots of $ x^3-3x+1$
negative_passages.docid: 62446
negative_passages.text: Solve the equation $x^2+\frac{9x^2}{(x+3)^2}=27$
negative_passages.docid: 124073
negative_passages.text: solving for one solution to a system of polynomials
negative_passages.docid: 20491
negative_passages.text: How to solve this equation $x^{2}=2^{x}$?
negative_passages.docid: 70147
negative_passages.text: Solving $x^4 -10x^3 + 26x^2 -10x +1 = 0$.
negative_passages.docid: 69328
negative_passages.text: (USAJMO)Find the integer solutions:$ab^5+3=x^3,a^5b+3=y^3$
negative_passages.docid: 54608
negative_passages.text: How to find all solutions of $4^x-3^x=1$?
negative_passages.docid: 114529
negative_passages.text: Factoring/Reducing a polynomial $x^4 -2x^3 + 2x^2 + x + 4$
negative_passages.docid: 134088
negative_passages.text: How to factorize $x^4+2x^2+4$ to a product of polynomials with real coefficients?
negative_passages.docid: 52278
negative_passages.text: How to solve $\sum_{k=2}^\infty {\frac{1}{k^2-1}}$
negative_passages.docid: 133680
negative_passages.text: On the equation $3x^3 + 4y^3 + 5z^3 = 0$
negative_passages.docid: 23726
negative_passages.text: A closed form for $1^{2}-2^{2}+3^{2}-4^{2}+ \cdots + (-1)^{n-1}n^{2}$
negative_passages.docid: 60589
negative_passages.text: Solve for $x$ in $6x^2-25x+12+\frac{25}{x}+\frac{6}{x^2}=0$