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=128+112S-(16S*S)
We move all terms to the left:
-(128+112S-(16S*S))=0
We add all the numbers together, and all the variables
-(128+112S-(+16S*S))=0
We calculate terms in parentheses: -(128+112S-(+16S*S)), so:We get rid of parentheses
128+112S-(+16S*S)
determiningTheFunctionDomain 112S-(+16S*S)+128
We get rid of parentheses
112S-16S*S+128
Wy multiply elements
-16S^2+112S+128
Back to the equation:
-(-16S^2+112S+128)
16S^2-112S-128=0
a = 16; b = -112; c = -128;
Δ = b2-4ac
Δ = -1122-4·16·(-128)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{20736}=144$$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-144}{2*16}=\frac{-32}{32} =-1 $$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+144}{2*16}=\frac{256}{32} =8 $
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