(2x)2−3=6 (2x)^2-3=6 (2x)2−3=6
First we rearrange the equation and set it to 0
4x2−3−6=0 4x^2-3-6=0 4x2−3−6=0
4x2−9=0 4x^2-9=0 4x2−9=0
We then apply the shortcut multiplication formula:
4(x2−94)=0 4(x^2-\frac{9}{4})=0 4(x2−49)=0
x2−(32)2=0 x^2-(\frac{3}{2})^2=0 x2−(23)2=0
(x−32)(x+32)=0 (x-\frac{3}{2})(x+\frac{3}{2})=0 (x−23)(x+23)=0
x=±32 x=\pm\frac{3}{2} x=±23
±32 ±\frac{3}{2} ±23