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1/2h+1/2h+1/4h+4=8
We move all terms to the left:
1/2h+1/2h+1/4h+4-(8)=0
Domain of the equation: 2h!=0
h!=0/2
h!=0
h∈R
Domain of the equation: 4h!=0We add all the numbers together, and all the variables
h!=0/4
h!=0
h∈R
1/2h+1/2h+1/4h-4=0
We calculate fractions
(4h+1)/8h^2+2h/8h^2-4=0
We multiply all the terms by the denominator
(4h+1)+2h-4*8h^2=0
We add all the numbers together, and all the variables
2h+(4h+1)-4*8h^2=0
Wy multiply elements
-32h^2+2h+(4h+1)=0
We get rid of parentheses
-32h^2+2h+4h+1=0
We add all the numbers together, and all the variables
-32h^2+6h+1=0
a = -32; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-32)·1
Δ = 164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{41}}{2*-32}=\frac{-6-2\sqrt{41}}{-64} $$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{41}}{2*-32}=\frac{-6+2\sqrt{41}}{-64} $
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