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x(0.5x+1)=0.4
We move all terms to the left:
x(0.5x+1)-(0.4)=0
We add all the numbers together, and all the variables
x(0.5x+1)-0.4=0
We multiply parentheses
0x^2+x-0.4=0
We add all the numbers together, and all the variables
x^2+x-0.4=0
a = 1; b = 1; c = -0.4;
Δ = b2-4ac
Δ = 12-4·1·(-0.4)
Δ = 2.6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{2.6}}{2*1}=\frac{-1-\sqrt{2.6}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2.6}}{2*1}=\frac{-1+\sqrt{2.6}}{2} $
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