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x(x-2)(x+2)=5760
We move all terms to the left:
x(x-2)(x+2)-(5760)=0
We use the square of the difference formula
x^2-4-5760=0
We add all the numbers together, and all the variables
x^2-5764=0
a = 1; b = 0; c = -5764;
Δ = b2-4ac
Δ = 02-4·1·(-5764)
Δ = 23056
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{23056}=\sqrt{16*1441}=\sqrt{16}*\sqrt{1441}=4\sqrt{1441}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1441}}{2*1}=\frac{0-4\sqrt{1441}}{2} =-\frac{4\sqrt{1441}}{2} =-2\sqrt{1441} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1441}}{2*1}=\frac{0+4\sqrt{1441}}{2} =\frac{4\sqrt{1441}}{2} =2\sqrt{1441} $
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