x = \sqrt { 0,082 } d a m ^ { 2 } + 4 \cdot 10 ^ { - 6 } k m ^ { 2 } + 3800 cm ^ { 2 }
Solve for a
\left\{\begin{matrix}a=-\frac{\sqrt{205}\left(950000000cm^{2}+km^{2}-250000x\right)}{1025000dm^{2}}\text{, }&d\neq 0\text{ and }m\neq 0\\a\in \mathrm{R}\text{, }&\left(x=0\text{ and }m=0\right)\text{ or }\left(x=\frac{\left(k+950000000c\right)m^{2}}{250000}\text{ and }d=0\right)\end{matrix}\right.
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x=\sqrt{0,082}dam^{2}+4\times \frac{1}{1000000}km^{2}+3800cm^{2}
Calculate 10 to the power of -6 and get \frac{1}{1000000}.
x=\sqrt{0,082}dam^{2}+\frac{1}{250000}km^{2}+3800cm^{2}
Multiply 4 and \frac{1}{1000000} to get \frac{1}{250000}.
\sqrt{0,082}dam^{2}+\frac{1}{250000}km^{2}+3800cm^{2}=x
Swap sides so that all variable terms are on the left hand side.
\sqrt{0,082}dam^{2}+3800cm^{2}=x-\frac{1}{250000}km^{2}
Subtract \frac{1}{250000}km^{2} from both sides.
\sqrt{0,082}dam^{2}=x-\frac{1}{250000}km^{2}-3800cm^{2}
Subtract 3800cm^{2} from both sides.
\sqrt{0,082}dm^{2}a=-\frac{km^{2}}{250000}-3800cm^{2}+x
The equation is in standard form.
\frac{\sqrt{0,082}dm^{2}a}{\sqrt{0,082}dm^{2}}=\frac{-\frac{km^{2}}{250000}-3800cm^{2}+x}{\sqrt{0,082}dm^{2}}
Divide both sides by \sqrt{0,082}dm^{2}.
a=\frac{-\frac{km^{2}}{250000}-3800cm^{2}+x}{\sqrt{0,082}dm^{2}}
Dividing by \sqrt{0,082}dm^{2} undoes the multiplication by \sqrt{0,082}dm^{2}.
a=\frac{\sqrt{205}\left(250000x-km^{2}-950000000cm^{2}\right)}{1025000dm^{2}}
Divide x-\frac{km^{2}}{250000}-3800cm^{2} by \sqrt{0,082}dm^{2}.
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