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X+1/2X+1/2X-5=35
We move all terms to the left:
X+1/2X+1/2X-5-(35)=0
Domain of the equation: 2X!=0We add all the numbers together, and all the variables
X!=0/2
X!=0
X∈R
X+1/2X+1/2X-40=0
We multiply all the terms by the denominator
X*2X-40*2X+1+1=0
We add all the numbers together, and all the variables
X*2X-40*2X+2=0
Wy multiply elements
2X^2-80X+2=0
a = 2; b = -80; c = +2;
Δ = b2-4ac
Δ = -802-4·2·2
Δ = 6384
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6384}=\sqrt{16*399}=\sqrt{16}*\sqrt{399}=4\sqrt{399}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{399}}{2*2}=\frac{80-4\sqrt{399}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{399}}{2*2}=\frac{80+4\sqrt{399}}{4} $
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