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0=2(x^2+4x-508)
We move all terms to the left:
0-(2(x^2+4x-508))=0
We add all the numbers together, and all the variables
-(2(x^2+4x-508))=0
We calculate terms in parentheses: -(2(x^2+4x-508)), so:We get rid of parentheses
2(x^2+4x-508)
We multiply parentheses
2x^2+8x-1016
Back to the equation:
-(2x^2+8x-1016)
-2x^2-8x+1016=0
a = -2; b = -8; c = +1016;
Δ = b2-4ac
Δ = -82-4·(-2)·1016
Δ = 8192
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-64\sqrt{2}}{2*-2}=\frac{8-64\sqrt{2}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+64\sqrt{2}}{2*-2}=\frac{8+64\sqrt{2}}{-4} $
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