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6x^2-11/114+x2=1
We move all terms to the left:
6x^2-11/114+x2-(1)=0
determiningTheFunctionDomain 6x^2+x2-1-11/114=0
We add all the numbers together, and all the variables
7x^2-1-11/114=0
We multiply all the terms by the denominator
7x^2*114-11-1*114=0
We add all the numbers together, and all the variables
7x^2*114-125=0
Wy multiply elements
798x^2-125=0
a = 798; b = 0; c = -125;
Δ = b2-4ac
Δ = 02-4·798·(-125)
Δ = 399000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{399000}=\sqrt{100*3990}=\sqrt{100}*\sqrt{3990}=10\sqrt{3990}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3990}}{2*798}=\frac{0-10\sqrt{3990}}{1596} =-\frac{10\sqrt{3990}}{1596} =-\frac{5\sqrt{3990}}{798} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3990}}{2*798}=\frac{0+10\sqrt{3990}}{1596} =\frac{10\sqrt{3990}}{1596} =\frac{5\sqrt{3990}}{798} $
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