Solve for x
x\in \begin{bmatrix}-\sqrt{2},\sqrt{2}\end{bmatrix}
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-2+x^{2}\leq 0
Multiply the inequality by -1 to make the coefficient of the highest power in 2-x^{2} positive. Since -1 is negative, the inequality direction is changed.
x^{2}\leq 2
Add 2 to both sides.
x^{2}\leq \left(\sqrt{2}\right)^{2}
Calculate the square root of 2 and get \sqrt{2}. Rewrite 2 as \left(\sqrt{2}\right)^{2}.
|x|\leq \sqrt{2}
Inequality holds for |x|\leq \sqrt{2}.
x\in \begin{bmatrix}-\sqrt{2},\sqrt{2}\end{bmatrix}
Rewrite |x|\leq \sqrt{2} as x\in \left[-\sqrt{2},\sqrt{2}\right].
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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