(X/2)(x)=162

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Solution for (X/2)(x)=162 equation:



(X/2)(X)=162
We move all terms to the left:
(X/2)(X)-(162)=0
Domain of the equation: 2)X!=0
X!=0/1
X!=0
X∈R
We add all the numbers together, and all the variables
(+X/2)X-162=0
We multiply parentheses
X^2-162=0
a = 1; b = 0; c = -162;
Δ = b2-4ac
Δ = 02-4·1·(-162)
Δ = 648
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:
$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{2}}{2*1}=\frac{0-18\sqrt{2}}{2} =-\frac{18\sqrt{2}}{2} =-9\sqrt{2} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{2}}{2*1}=\frac{0+18\sqrt{2}}{2} =\frac{18\sqrt{2}}{2} =9\sqrt{2} $

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