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0.1886=w(1-0.59w)
We move all terms to the left:
0.1886-(w(1-0.59w))=0
We add all the numbers together, and all the variables
-(w(-0.59w+1))+0.1886=0
We calculate terms in parentheses: -(w(-0.59w+1)), so:We get rid of parentheses
w(-0.59w+1)
We multiply parentheses
0w^2+w
We add all the numbers together, and all the variables
w^2+w
Back to the equation:
-(w^2+w)
-w^2-w+0.1886=0
We add all the numbers together, and all the variables
-1w^2-1w+0.1886=0
a = -1; b = -1; c = +0.1886;
Δ = b2-4ac
Δ = -12-4·(-1)·0.1886
Δ = 1.7544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{1.7544}}{2*-1}=\frac{1-\sqrt{1.7544}}{-2} $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1.7544}}{2*-1}=\frac{1+\sqrt{1.7544}}{-2} $
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