Solve for x
x=\frac{1}{2}=0.5
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\left(2x\right)^{2}-9-x\left(4x-18\right)=0
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.
2^{2}x^{2}-9-x\left(4x-18\right)=0
Expand \left(2x\right)^{2}.
4x^{2}-9-x\left(4x-18\right)=0
Calculate 2 to the power of 2 and get 4.
4x^{2}-9-\left(4x^{2}-18x\right)=0
Use the distributive property to multiply x by 4x-18.
4x^{2}-9-4x^{2}+18x=0
To find the opposite of 4x^{2}-18x, find the opposite of each term.
-9+18x=0
Combine 4x^{2} and -4x^{2} to get 0.
18x=9
Add 9 to both sides. Anything plus zero gives itself.
x=\frac{9}{18}
Divide both sides by 18.
x=\frac{1}{2}
Reduce the fraction \frac{9}{18} to lowest terms by extracting and canceling out 9.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
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}