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2x+1/2x=35
We move all terms to the left:
2x+1/2x-(35)=0
Domain of the equation: 2x!=0We multiply all the terms by the denominator
x!=0/2
x!=0
x∈R
2x*2x-35*2x+1=0
Wy multiply elements
4x^2-70x+1=0
a = 4; b = -70; c = +1;
Δ = b2-4ac
Δ = -702-4·4·1
Δ = 4884
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4884}=\sqrt{4*1221}=\sqrt{4}*\sqrt{1221}=2\sqrt{1221}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1221}}{2*4}=\frac{70-2\sqrt{1221}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1221}}{2*4}=\frac{70+2\sqrt{1221}}{8} $
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