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x^2+16x^2=208
We move all terms to the left:
x^2+16x^2-(208)=0
We add all the numbers together, and all the variables
17x^2-208=0
a = 17; b = 0; c = -208;
Δ = b2-4ac
Δ = 02-4·17·(-208)
Δ = 14144
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14144}=\sqrt{64*221}=\sqrt{64}*\sqrt{221}=8\sqrt{221}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{221}}{2*17}=\frac{0-8\sqrt{221}}{34} =-\frac{8\sqrt{221}}{34} =-\frac{4\sqrt{221}}{17} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{221}}{2*17}=\frac{0+8\sqrt{221}}{34} =\frac{8\sqrt{221}}{34} =\frac{4\sqrt{221}}{17} $
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