Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{2x-\alpha +2}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }\alpha =2\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{2x-\alpha +2}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }\alpha =2\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{a\alpha -2a+1}-1}{a}\text{; }x=-\frac{\sqrt{a\alpha -2a+1}+1}{a}\text{, }&a\neq 0\\x=\frac{\alpha -2}{2}\text{, }&a=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{a\alpha -2a+1}-1}{a}\text{; }x=-\frac{\sqrt{a\alpha -2a+1}+1}{a}\text{, }&\left(a\neq 0\text{ and }\alpha =2\right)\text{ or }\left(a\neq 0\text{ and }\alpha \leq 2\text{ and }a\leq -\frac{1}{\alpha -2}\right)\text{ or }\left(a\neq 0\text{ and }a\geq -\frac{1}{\alpha -2}\text{ and }\alpha \geq 2\right)\text{ or }\left(\alpha \neq 2\text{ and }a=-\frac{1}{\alpha -2}\right)\\x=\frac{\alpha -2}{2}\text{, }&a=0\end{matrix}\right.
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ax^{2}+2x-\alpha +2=0
To find the opposite of \alpha -2, find the opposite of each term.
ax^{2}-\alpha +2=-2x
Subtract 2x from both sides. Anything subtracted from zero gives its negation.
ax^{2}+2=-2x+\alpha
Add \alpha to both sides.
ax^{2}=-2x+\alpha -2
Subtract 2 from both sides.
x^{2}a=-2x+\alpha -2
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{-2x+\alpha -2}{x^{2}}
Divide both sides by x^{2}.
a=\frac{-2x+\alpha -2}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
ax^{2}+2x-\alpha +2=0
To find the opposite of \alpha -2, find the opposite of each term.
ax^{2}-\alpha +2=-2x
Subtract 2x from both sides. Anything subtracted from zero gives its negation.
ax^{2}+2=-2x+\alpha
Add \alpha to both sides.
ax^{2}=-2x+\alpha -2
Subtract 2 from both sides.
x^{2}a=-2x+\alpha -2
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{-2x+\alpha -2}{x^{2}}
Divide both sides by x^{2}.
a=\frac{-2x+\alpha -2}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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}