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20000=x*1.0275^3
We move all terms to the left:
20000-(x*1.0275^3)=0
We get rid of parentheses
-x*1.0275^3+20000=0
Wy multiply elements
-1x^2+20000=0
a = -1; b = 0; c = +20000;
Δ = b2-4ac
Δ = 02-4·(-1)·20000
Δ = 80000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80000}=\sqrt{40000*2}=\sqrt{40000}*\sqrt{2}=200\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{2}}{2*-1}=\frac{0-200\sqrt{2}}{-2} =-\frac{200\sqrt{2}}{-2} =-\frac{100\sqrt{2}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{2}}{2*-1}=\frac{0+200\sqrt{2}}{-2} =\frac{200\sqrt{2}}{-2} =\frac{100\sqrt{2}}{-1} $
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