Solve for x
x = \frac{3}{2} = 1\frac{1}{2} = 1.5
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Linear Equation
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( \sqrt { 2 } x - 3 ) ( \sqrt { 2 } x + 3 ) = 2 x ( x - 3 )
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\left(\sqrt{2}x\right)^{2}-9=2x\left(x-3\right)
Consider \left(\sqrt{2}x-3\right)\left(\sqrt{2}x+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.
\left(\sqrt{2}\right)^{2}x^{2}-9=2x\left(x-3\right)
Expand \left(\sqrt{2}x\right)^{2}.
2x^{2}-9=2x\left(x-3\right)
The square of \sqrt{2} is 2.
2x^{2}-9=2x^{2}-6x
Use the distributive property to multiply 2x by x-3.
2x^{2}-9-2x^{2}=-6x
Subtract 2x^{2} from both sides.
-9=-6x
Combine 2x^{2} and -2x^{2} to get 0.
-6x=-9
Swap sides so that all variable terms are on the left hand side.
x=\frac{-9}{-6}
Divide both sides by -6.
x=\frac{3}{2}
Reduce the fraction \frac{-9}{-6} to lowest terms by extracting and canceling out -3.
Examples
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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
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