X²+6x+9-2x²+8x-49≥0
-x²+14x-40≥0
x²-14x+40≤0
Д=196-160=36
x1=(14-6)/2=4
x2=(14+6)/2=10
(x-4)(x-10)≤0
Это выполняется в двух случаях
1)
\left \{ {{x \leq 4} \atop {x \geq 10}} \right. " alt=" \left \{ {{x-4 \leq 0} \atop {x-10 \geq 0}} \right. <=> \left \{ {{x \leq 4} \atop {x \geq 10}} \right. " align="absmiddle" class="latex-formula"> решений нет
2)
\left \{ {{x \geq 4} \atop {x \leq 10}} \right. " alt=" \left \{ {{x-4 \geq 0} \atop {x-10 \leq 0}} \right.<=> \left \{ {{x \geq 4} \atop {x \leq 10}} \right. " align="absmiddle" class="latex-formula">
решение x∈[4;10]