2x2+8x+16=64

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Solution for 2x2+8x+16=64 equation:



2x^2+8x+16=64
We move all terms to the left:
2x^2+8x+16-(64)=0
We add all the numbers together, and all the variables
2x^2+8x-48=0
a = 2; b = 8; c = -48;
Δ = b2-4ac
Δ = 82-4·2·(-48)
Δ = 448
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:
$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{7}}{2*2}=\frac{-8-8\sqrt{7}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{7}}{2*2}=\frac{-8+8\sqrt{7}}{4} $

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