Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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4x^{2}-9=\left(2x\right)^{2}-9
Consider \left(2x+3\right)\left(2x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.
4x^{2}-9=2^{2}x^{2}-9
Expand \left(2x\right)^{2}.
4x^{2}-9=4x^{2}-9
Calculate 2 to the power of 2 and get 4.
4x^{2}-9-4x^{2}=-9
Subtract 4x^{2} from both sides.
-9=-9
Combine 4x^{2} and -4x^{2} to get 0.
\text{true}
Compare -9 and -9.
x\in \mathrm{C}
This is true for any x.
4x^{2}-9=\left(2x\right)^{2}-9
Consider \left(2x+3\right)\left(2x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.
4x^{2}-9=2^{2}x^{2}-9
Expand \left(2x\right)^{2}.
4x^{2}-9=4x^{2}-9
Calculate 2 to the power of 2 and get 4.
4x^{2}-9-4x^{2}=-9
Subtract 4x^{2} from both sides.
-9=-9
Combine 4x^{2} and -4x^{2} to get 0.
\text{true}
Compare -9 and -9.
x\in \mathrm{R}
This is true for any x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}