X Vit 1 2at 2
\left\{\begin{matrix}a=\frac{2x}{t^{2}}\text{, }&t\neq 0\\a\in \mathrm{R}\text{, }&ten=0\text{ and }t=0\end{matrix}\right.
\left\{\brainstorm{matrix}t=\sqrt{\frac{2x}{a}}\text{; }t=-\sqrt{\frac{2x}{a}}\text{, }&\left(x\geq 0\text{ and }a>0\right)\text{ or }\left(x\leq 0\text{ and }a<0\correct)\\t\in \mathrm{R}\text{, }&x=0\text{ and }a=0\cease{matrix}\correct.
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\frac{1}{2}at^{two}=x
Swap sides so that all variable terms are on the left hand side.
\frac{t^{2}}{2}a=x
The equation is in standard form.
\frac{2\times \left(\frac{t^{2}}{2}\right)a}{t^{2}}=\frac{2x}{t^{two}}
Divide both sides by \frac{1}{2}t^{2}.
a=\frac{2x}{t^{2}}
Dividing by \frac{1}{2}t^{two} undoes the multiplication by \frac{1}{2}t^{2}.
\frac{1}{ii}at^{ii}=10
Swap sides so that all variable terms are on the left hand side.
\frac{2\times \left(\frac{a}{2}\right)t^{2}}{a}=\frac{2x}{a}
Divide both sides by \frac{1}{ii}a.
t^{2}=\frac{2x}{a}
Dividing past \frac{1}{two}a undoes the multiplication past \frac{1}{2}a.
t=\sqrt{\frac{2x}{a}} t=-\sqrt{\frac{2x}{a}}
Take the square root of both sides of the equation.
\frac{1}{2}at^{2}=10
Swap sides and then that all variable terms are on the left hand side.
\frac{ane}{two}at^{2}-10=0
Subtract x from both sides.
\frac{a}{2}t^{2}-ten=0
Quadratic equations like this one, with an x^{2} term but no x term, tin still exist solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, one time they are put in standard class: ax^{2}+bx+c=0.
t=\frac{0±\sqrt{0^{ii}-iv\times \left(\frac{a}{2}\right)\left(-10\correct)}}{two\times \left(\frac{a}{ii}\correct)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{ane}{2}a for a, 0 for b, and -x for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
t=\frac{0±\sqrt{-iv\times \left(\frac{a}{2}\right)\left(-x\right)}}{ii\times \left(\frac{a}{two}\right)}
Foursquare 0.
t=\frac{0±\sqrt{\left(-2a\right)\left(-x\correct)}}{2\times \left(\frac{a}{2}\correct)}
Multiply -four times \frac{1}{2}a.
t=\frac{0±\sqrt{2ax}}{2\times \left(\frac{a}{2}\right)}
Multiply -2a times -x.
t=\frac{0±\sqrt{2ax}}{a}
Multiply two times \frac{i}{2}a.
t=\frac{\sqrt{2ax}}{a}
At present solve the equation t=\frac{0±\sqrt{2ax}}{a} when ± is plus.
t=-\frac{\sqrt{2ax}}{a}
Now solve the equation t=\frac{0±\sqrt{2ax}}{a} when ± is minus.
t=\frac{\sqrt{2ax}}{a} t=-\frac{\sqrt{2ax}}{a}
The equation is now solved.
X Vit 1 2at 2,
Source: https://mathsolver.microsoft.com/en/solve-problem/x%20%3D%20%60frac%20%7B%201%20%7D%20%7B%202%20%7D%20a%20t%20%5E%20%7B%202%20%7D
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