y - t = - \sqrt { ( } \quad - s )
Solve for s
s=-\left(y-t\right)^{2}
-\left(y-t\right)\geq 0
Solve for t
t=y+\sqrt{-s}
s\leq 0
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-\sqrt{-s}=y-t
Swap sides so that all variable terms are on the left hand side.
\frac{-\sqrt{-s}}{-1}=\frac{y-t}{-1}
Divide both sides by -1.
\sqrt{-s}=\frac{y-t}{-1}
Dividing by -1 undoes the multiplication by -1.
\sqrt{-s}=t-y
Divide y-t by -1.
-s=\left(t-y\right)^{2}
Square both sides of the equation.
\frac{-s}{-1}=\frac{\left(t-y\right)^{2}}{-1}
Divide both sides by -1.
s=\frac{\left(t-y\right)^{2}}{-1}
Dividing by -1 undoes the multiplication by -1.
s=-\left(t-y\right)^{2}
Divide \left(-y+t\right)^{2} by -1.
-t=-\sqrt{-s}-y
Subtract y from both sides.
-t=-y-\sqrt{-s}
The equation is in standard form.
\frac{-t}{-1}=\frac{-y-\sqrt{-s}}{-1}
Divide both sides by -1.
t=\frac{-y-\sqrt{-s}}{-1}
Dividing by -1 undoes the multiplication by -1.
t=y+\sqrt{-s}
Divide -\sqrt{-s}-y by -1.
Examples
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{ 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}