Solve for p
p=-\frac{x^{2}}{1-x}
x\neq 1
Solve for x (complex solution)
x=\frac{\sqrt{p\left(p-4\right)}+p}{2}
x=\frac{-\sqrt{p\left(p-4\right)}+p}{2}
Solve for x
x=\frac{\sqrt{p\left(p-4\right)}+p}{2}
x=\frac{-\sqrt{p\left(p-4\right)}+p}{2}\text{, }p\geq 4\text{ or }p\leq 0
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-px+p=-x^{2}
Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.
\left(-x+1\right)p=-x^{2}
Combine all terms containing p.
\left(1-x\right)p=-x^{2}
The equation is in standard form.
\frac{\left(1-x\right)p}{1-x}=-\frac{x^{2}}{1-x}
Divide both sides by -x+1.
p=-\frac{x^{2}}{1-x}
Dividing by -x+1 undoes the multiplication by -x+1.
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}