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X+1/2X=133
We move all terms to the left:
X+1/2X-(133)=0
Domain of the equation: 2X!=0We multiply all the terms by the denominator
X!=0/2
X!=0
X∈R
X*2X-133*2X+1=0
Wy multiply elements
2X^2-266X+1=0
a = 2; b = -266; c = +1;
Δ = b2-4ac
Δ = -2662-4·2·1
Δ = 70748
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{70748}=\sqrt{4*17687}=\sqrt{4}*\sqrt{17687}=2\sqrt{17687}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-266)-2\sqrt{17687}}{2*2}=\frac{266-2\sqrt{17687}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-266)+2\sqrt{17687}}{2*2}=\frac{266+2\sqrt{17687}}{4} $
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