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1/2x+1/2x=x+2
We move all terms to the left:
1/2x+1/2x-(x+2)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
1/2x+1/2x-x-2=0
We multiply all the terms by the denominator
-x*2x-2*2x+1+1=0
We add all the numbers together, and all the variables
-x*2x-2*2x+2=0
Wy multiply elements
-2x^2-4x+2=0
a = -2; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-2)·2
Δ = 32
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2}}{2*-2}=\frac{4-4\sqrt{2}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2}}{2*-2}=\frac{4+4\sqrt{2}}{-4} $
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