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-81x^2=-11
We move all terms to the left:
-81x^2-(-11)=0
We add all the numbers together, and all the variables
-81x^2+11=0
a = -81; b = 0; c = +11;
Δ = b2-4ac
Δ = 02-4·(-81)·11
Δ = 3564
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3564}=\sqrt{324*11}=\sqrt{324}*\sqrt{11}=18\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{11}}{2*-81}=\frac{0-18\sqrt{11}}{-162} =-\frac{18\sqrt{11}}{-162} =-\frac{\sqrt{11}}{-9} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{11}}{2*-81}=\frac{0+18\sqrt{11}}{-162} =\frac{18\sqrt{11}}{-162} =\frac{\sqrt{11}}{-9} $
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