Решение уравнение 1)х^2= -9х-8 2) х^2-20х=-5х-13-х^2 3)х^2-6х=5х-12-х^2 4)х^2-11х=-15х+6-х^2

1)[latex] x^{2} =-9x-8[/latex] [latex] x^{2} +9x+8=0[/latex] [latex]D= b^{2} -4ac= 9^{2} -4*1*8=81-32=49[/latex] [latex] x_{1,2} = \frac{-b+- \sqrt{D} }{2a}= \frac{-9+- \sqrt{49} }{2*1}= \frac{-9+-7}{2}= \left \{ {{x=-8} \atop {x=-1}} \right. [/latex] Ответ: -8; -1 2)[latex] x^{2} -20x=-5x-13- x^{2} [/latex] [latex] x^{2} -20x+5x+13+ x^{2} =0[/latex] [latex]2 x^{2} -15x+13=0[/latex] [latex]D= b^{2} -4ac= (-15)^{2} -4*2*13=225-104=121[/latex] [latex] x_{1,2} = \frac{-b+- \sqrt{D} }{2a}= \frac{15+- \sqrt{121} }{2*2}= \frac{15+-11}{4}= \left \{ {{x=6.5} \atop {x=1}} \right. [/latex] Ответ: 1; 6.5 3)[latex] x^{2} -6x=5x-12- x^{2} [/latex] [latex] x^{2} -6x-5x+12+ x^{2} =0[/latex] [latex]2 x^{2} -11x+12=0[/latex] [latex]D= b^{2} -4ac= (-11)^{2} -4*2*12=121-96=25[/latex] [latex] x_{1,2}= \frac{-b+- \sqrt{D} }{2a}= \frac{11+- \sqrt{25} }{2*2}= \frac{11+-5}{4}= \left \{ {{x=4} \atop {x=1.5}} \right. [/latex] Ответ:1.5;4 4)[latex] x^{2} -11x=-15x+6- x^{2} [/latex] [latex] x^{2} -11x+15x-6+ x^{2} =0[/latex] [latex]2 x^{2} +4x-6=0[/latex] [latex]D= b^{2}-4ac= 4^{2} -4*2*(-6)=16+48=64[/latex] [latex] x_{1,2} = \frac{-b+- \sqrt{D} }{2a}= \frac{-4+- \sqrt{64} }{2*2}= \frac{-4+-8}{4}= \left \{ {{x=-3} \atop {x=1}} \right. [/latex] Ответ:-3;1