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Use completion of squares to determine the solution of 4x^2 - 2x + 16 = 0

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tonyah995 | Student, Undergraduate | (Level 1) Salutatorian

Posted September 12, 2013 at 12:31 PM via web

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Use completion of squares to determine the solution of 4x^2 - 2x + 16 = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 12, 2013 at 12:36 PM (Answer #1)

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The equation 4x^2 - 2x + 16 = 0 has to be solved.

4x^2 - 2x + 16 = 0

=> `(2x)^2 - 2*2x*(1/2) + 16 = 0`

=> `(2x)^2 - 2*2x*(1/2) + (1/2)^2 + 16 = 1/4`

=> `(2x)^2 - 2*2x*(1/2) + (1/2)^2 = 1/4 - 16`

=> `(2x - 1/2)^2 = -63/4`

=> `2x - 1/2 = +-sqrt(-63/4)`

=> `2x - 1/2 = (+-i*sqrt 63)/2`

=> `2x = 1/2 +- (i*sqrt 63)/2`

=> `x = 1/4 +- i*sqrt 63/4`

The solution of the equation 4x^2 - 2x + 16 = 0 is `1/4 +- i*sqrt 63/4`

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