Solve for x
x = \frac{\sqrt{6}}{2} \approx 1.224744871
x = -\frac{\sqrt{6}}{2} \approx -1.224744871
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x^{2}\times 2=3
Multiply x and x to get x^{2}.
x^{2}=\frac{3}{2}
Divide both sides by 2.
x=\frac{\sqrt{6}}{2} x=-\frac{\sqrt{6}}{2}
Take the square root of both sides of the equation.
x^{2}\times 2=3
Multiply x and x to get x^{2}.
x^{2}\times 2-3=0
Subtract 3 from both sides.
2x^{2}-3=0
Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.
x=\frac{0±\sqrt{0^{2}-4\times 2\left(-3\right)}}{2\times 2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 2\left(-3\right)}}{2\times 2}
Square 0.
x=\frac{0±\sqrt{-8\left(-3\right)}}{2\times 2}
Multiply -4 times 2.
x=\frac{0±\sqrt{24}}{2\times 2}
Multiply -8 times -3.
x=\frac{0±2\sqrt{6}}{2\times 2}
Take the square root of 24.
x=\frac{0±2\sqrt{6}}{4}
Multiply 2 times 2.
x=\frac{\sqrt{6}}{2}
Now solve the equation x=\frac{0±2\sqrt{6}}{4} when ± is plus.
x=-\frac{\sqrt{6}}{2}
Now solve the equation x=\frac{0±2\sqrt{6}}{4} when ± is minus.
x=\frac{\sqrt{6}}{2} x=-\frac{\sqrt{6}}{2}
The equation is now solved.
Examples
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Linear equation
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Matrix
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}