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110=x(.1x)
We move all terms to the left:
110-(x(.1x))=0
We add all the numbers together, and all the variables
-(x(+.1x))+110=0
We calculate terms in parentheses: -(x(+.1x)), so:We add all the numbers together, and all the variables
x(+.1x)
We multiply parentheses
x^2
Back to the equation:
-(x^2)
-1x^2+110=0
a = -1; b = 0; c = +110;
Δ = b2-4ac
Δ = 02-4·(-1)·110
Δ = 440
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{110}}{2*-1}=\frac{0-2\sqrt{110}}{-2} =-\frac{2\sqrt{110}}{-2} =-\frac{\sqrt{110}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{110}}{2*-1}=\frac{0+2\sqrt{110}}{-2} =\frac{2\sqrt{110}}{-2} =\frac{\sqrt{110}}{-1} $
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