(2x)2−3=6 (2x)^2-3=6 (2x)2−3=6
±43 ±\frac{4}{3} ±34
±32 ±\frac{3}{2} ±23
(x+7)(x−7)3=−11−x2 \frac{(x+7)(x-7)}{3}=-11-x^2 3(x+7)(x−7)=−11−x2
±2
7
2x2−328=x+42 \frac{2x^2-32}{8}=\frac{x+4}{2} 82x2−32=2x+4
6
4
Solve the following:
x(x2−9)x2+3x=0 \frac{x(x^2-9)}{x^2+3x}=0 x2+3xx(x2−9)=0
3
±3
x2−64x−8=17(x+8)64−x2 \frac{x^2-64}{x-8}=\frac{17(x+8)}{64-x^2} x−8x2−64=64−x217(x+8)
±47 ±\sqrt{47} ±47
−9 -9 −9
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