Help with this quadratic formula?

Question

I am confused with this problem which is 8x^2 + 1 = 5x. The next step is 8x^2 - 5x = -1, then 8x^2 - 5x/2 + 25/4 = -1 + 25/4, this is were I get confused. Due you find LCD to complete this? Please can some help and explain this problem to me?

Answer 1

8x^2 + 1 = 5x
8x^2 - 5x + 1 = 0

x = (-b ± sqrt(b^2 - 4ac))/2a
a = 8
b = -5
c = 1

x = (-(-5) ± sqrt((-5)^2 - 4(8)(1)))/(2(8))
x = (5 ± sqrt(25 - 32))/16
x = (5 ± sqrt(-7))/16
x = (5 ± isqrt(7))/16
x = (1/16)(5 + isqrt(7)) or (1/16)(5 - isqrt(7))

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Using completing the square method

8x^2 + 1 = 5x
8x^2 - 5x = -1

divide everything by 8

x^2 - (5/8)x = (-1/8)

find half of (5/8), which is (5/16), square it, which gives you (25/256), and add to both sides

x^2 - (5/8)x + (25/256) = (-7/256)

factor the left side into a perfect square

(x - (5/16))^2 = (-7/256)

sqrt both sides

x - (5/16) = ±(1/16)(sqrt(-7))

add (5/16) to both sides

x = (5/16) ± (1/16)sqrt(-7)
x = (5/16) ± (i/16)sqrt(7)

same as saying

x = (1/16)(5 ± isqrt(7))

Answer 2

The third step is an error. Adding 25/4 to both sides is ok, but suddenly changing 5x to 5x/2 is not....

Answer 3

{ 5 ± Sq Root ( 25 - 32 ) } ÷ 16

Answer 4

Get everything to one side and have it equal to zero and use the quadratic formula to solve for x.