Question

$(x - 4) {2} > x(x + 12)$
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Answer 1

$(x-4)2 > x(x-12) \\ \\ 2x-8>x\left(x-12\right) \\ \\ 2x-8>x^{2}-12x \\ \\ 2x-8-x^{2}>-12x \\ \\ 2x-8-x^{2}+12x>0 \\ \\ 14x-8-x^{2}>0 \\ \\ -14x+8+x^{2}<0$

$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 1\times 8}}{2}$

$x=\frac{14±2\sqrt{41}}{2}$

$x=\sqrt{41}+7 x=7-\sqrt{41}$

$\left(x-\left(\sqrt{41}+7\right)\right)\left(x-\left(7-\sqrt{41}\right)\right)<0$

$x-\left(7-\sqrt{41}\right)>0 x-\left(\sqrt{41}+7\right)<0$

$x\in \left(7-\sqrt{41},\sqrt{41}+7\right)$

$x\in \left(7-\sqrt{41},\sqrt{41}+7\right)$