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Solve the quadratic equation by completing the square.

2x^2+2=3x

Express your answer in simplified form.

 Jan 19, 2019
 #1
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"Solve the quadratic equation by completing the square.

2x^2+2=3x"

 

Divide through by 2

x^2 + 1 = 3x/2

 

Rearrange

x^2 - 3x/2 = -1

 

Add  (1/2*3/2)^2 to both sides:

x^2 - 3x/2 + (1/2*3/2)^2 = (1/2*3/2)^2 - 1  or  x^2 - 3x/2 +9/16 = -7/16

 

Equation can now be written as (x - 3/4)^2 = -7/16

 

Hence   x = 3/4 ± √(-7/16)    or  x = (3 ± i√7)/4

.

 Jan 19, 2019

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