解方程 $4(2x-5)^2 - 105 = 0$。 答案 x = ___ 或 ___

1. Isolate the squared term.

$4(2x-5)^2-105=0$

$4(2x-5)^2=105$

$(2x-5)^2=\dfrac{105}{4}$

2. Take square roots and solve the resulting linear equations for $x$.

$2x-5=\pm\sqrt{\dfrac{105}{4}}$

$2x-5=\pm\dfrac{\sqrt{105}}{2}$

$2x=5\pm\dfrac{\sqrt{105}}{2}$

$x=\dfrac{5}{2}\pm\dfrac{\sqrt{105}}{4}$

So, $x=\dfrac{10+\sqrt{105}}{4}$ or $x=\dfrac{10-\sqrt{105}}{4}$.