[tex]x^2+15x+54\geq0 \wedge \sqrt{-x^2-2x+80}\not =0 \wedge -x^2-2x+80\geq 0\\x^2+7x+8x+54\geq0 \wedge -x^2-2x+80 > 0\\x(x+7)+8(x+7)\geq0 \wedge x^2+2x-80 < 0\\(x+8)(x+7)\geq0 \wedge x^2-8x+10x-80 < 0\\x\in(-\infty,-8\rangle\cup\langle-7,\infty)\wedge x(x-8)+10(x-8) < 0\\x\in(-\infty,-8\rangle\cup\langle-7,\infty)\wedge (x+10)(x-8) < 0\\x\in(-\infty,-8\rangle\cup\langle-7,\infty)\wedge x\in(-10,8)\\\boxed{x\in(-10,-8\rangle\cup\langle-7,8)}[/tex]
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[tex]x^2+15x+54\geq0 \wedge \sqrt{-x^2-2x+80}\not =0 \wedge -x^2-2x+80\geq 0\\x^2+7x+8x+54\geq0 \wedge -x^2-2x+80 > 0\\x(x+7)+8(x+7)\geq0 \wedge x^2+2x-80 < 0\\(x+8)(x+7)\geq0 \wedge x^2-8x+10x-80 < 0\\x\in(-\infty,-8\rangle\cup\langle-7,\infty)\wedge x(x-8)+10(x-8) < 0\\x\in(-\infty,-8\rangle\cup\langle-7,\infty)\wedge (x+10)(x-8) < 0\\x\in(-\infty,-8\rangle\cup\langle-7,\infty)\wedge x\in(-10,8)\\\boxed{x\in(-10,-8\rangle\cup\langle-7,8)}[/tex]