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use of quadratic formula to solve the following

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use quadratic formula to solve 8x^2 + 4x + 1 = 0

Guest Oct 3, 2017
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Solve for x:
8 x^2 + 4 x + 1 = 0

x = (-4 ± sqrt(4^2 - 4×8))/(2×8) = (-4 ± sqrt(16 - 32))/16 = (-4 ± sqrt(-16))/16:
x = (-4 + sqrt(-16))/16 or x = (-4 - sqrt(-16))/16

sqrt(-16) = sqrt(-1) sqrt(16) = i sqrt(16):
x = (-4 + i sqrt(16))/16 or x = (-4 - i sqrt(16))/16

sqrt(16) = sqrt(2^4) = 4 = 4:
x = (-4 + i×4)/16 or x = (-4 - i×4)/16

Factor 4 from -4 + 4 i giving -4 + 4 i:
x = -4 + 4 i/16 or x = (-4 - 4 i)/16

(4 i - 4)/16 = (4 i - 4)/(4×4) = (i - 1)/4:
x = -1/4 + i/4 or x = (-4 - 4 i)/16

Factor 4 from -4 - 4 i giving -4 - 4 i:
x = -1/4 + i/4 or x = -4 - 4 i/16

(-(4 i) - 4)/16 = (-(4 i) - 4)/(4×4) = (-i - 1)/4:
x = -1/4 + i/4       or          x = -1/4 - i/4

Guest Oct 3, 2017

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