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4y=38-(1/2)(4y+16)
We move all terms to the left:
4y-(38-(1/2)(4y+16))=0
Domain of the equation: 2)(4y+16))!=0We add all the numbers together, and all the variables
y∈R
4y-(38-(+1/2)(4y+16))=0
We multiply parentheses ..
-(38-(+4y^2+1/2*16))+4y=0
We multiply all the terms by the denominator
-(38-(+4y^2+1+4y*2*16))=0
We calculate terms in parentheses: -(38-(+4y^2+1+4y*2*16)), so:We get rid of parentheses
38-(+4y^2+1+4y*2*16)
determiningTheFunctionDomain -(+4y^2+1+4y*2*16)+38
We get rid of parentheses
-4y^2-4y*2*16-1+38
We add all the numbers together, and all the variables
-4y^2-4y*2*16+37
Wy multiply elements
-4y^2-128y*1+37
Wy multiply elements
-4y^2-128y+37
Back to the equation:
-(-4y^2-128y+37)
4y^2+128y-37=0
a = 4; b = 128; c = -37;
Δ = b2-4ac
Δ = 1282-4·4·(-37)
Δ = 16976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16976}=\sqrt{16*1061}=\sqrt{16}*\sqrt{1061}=4\sqrt{1061}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-4\sqrt{1061}}{2*4}=\frac{-128-4\sqrt{1061}}{8} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+4\sqrt{1061}}{2*4}=\frac{-128+4\sqrt{1061}}{8} $
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