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4x+1/2x=188
We move all terms to the left:
4x+1/2x-(188)=0
Domain of the equation: 2x!=0We multiply all the terms by the denominator
x!=0/2
x!=0
x∈R
4x*2x-188*2x+1=0
Wy multiply elements
8x^2-376x+1=0
a = 8; b = -376; c = +1;
Δ = b2-4ac
Δ = -3762-4·8·1
Δ = 141344
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{141344}=\sqrt{16*8834}=\sqrt{16}*\sqrt{8834}=4\sqrt{8834}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-376)-4\sqrt{8834}}{2*8}=\frac{376-4\sqrt{8834}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-376)+4\sqrt{8834}}{2*8}=\frac{376+4\sqrt{8834}}{16} $
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