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1/2k+2=5+5-6k
We move all terms to the left:
1/2k+2-(5+5-6k)=0
Domain of the equation: 2k!=0We add all the numbers together, and all the variables
k!=0/2
k!=0
k∈R
1/2k-(-6k+10)+2=0
We get rid of parentheses
1/2k+6k-10+2=0
We multiply all the terms by the denominator
6k*2k-10*2k+2*2k+1=0
Wy multiply elements
12k^2-20k+4k+1=0
We add all the numbers together, and all the variables
12k^2-16k+1=0
a = 12; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·12·1
Δ = 208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{13}}{2*12}=\frac{16-4\sqrt{13}}{24} $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{13}}{2*12}=\frac{16+4\sqrt{13}}{24} $
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