[latex]x+ \sqrt{x+18} \leq 2[/latex]

[latex]x+ \sqrt{x+18} \leq 2[/latex] [latex] \sqrt{x+18} \leq 2-x[/latex] [latex] \left \{ {{x+18 \geq 0} \atop {2-x \geq 0}} \atop {( \sqrt{x+18})^2 \leq (2-x)^2}} \right. [/latex] [latex] \left \{ {{x \geq -18} \atop {x \leq 2}} \atop {x+18 \leq4+x^2-4x}} \right. [/latex] [latex] \left \{ {{x \geq -18} \atop {x \leq 2}} \atop {-x^2+5x+14 \leq0}} \right. [/latex] [latex]\left \{ {{x \geq -18} \atop {x \leq 2}} \atop {x^2-5x-14 \geq 0}} \right. [/latex] [latex]x^2-5x-14=0[/latex] [latex]D=(-5)^2-4*1*(-14)=25+56=81[/latex] [latex]x_1= \frac{5+9}{2}=7 [/latex] [latex]x_1= \frac{5-9}{2}=-2 [/latex] -----------[-18]------------------------[2]------------------------------                  //////////////////////////////// ---------+-----------[-2]----------------------[7]-------------+---------- ///////////////////////                                  /////////////////////////// Ответ: [ -18; -2]