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NotSoSmart  Nov 17, 2017
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Solve for x:
2 x^2 - 3 x + 2 = 0

Divide both sides by 2:
x^2 - (3 x)/2 + 1 = 0

 

Subtract 1 from both sides:
x^2 - (3 x)/2 = -1

 

Add 9/16 to both sides:
x^2 - (3 x)/2 + 9/16 = -7/16

 

Write the left hand side as a square:
(x - 3/4)^2 = -7/16

 

Take the square root of both sides:
x - 3/4 = (i sqrt(7))/4 or x - 3/4 = 1/4 (-i) sqrt(7)

Add 3/4 to both sides:


x = 3/4 + (i sqrt(7))/4 or x - 3/4 = 1/4 (-i) sqrt(7)

Add 3/4 to both sides:


x = 3/4 + (i sqrt(7))/4        or           x= 3/4 - (i sqrt(7))/4

 

 

Solve for x:
x^2 - 4 x - 5 = 0

 

The left hand side factors into a product with two terms:
(x - 5) (x + 1) = 0

 

Split into two equations:
x - 5 = 0 or x + 1 = 0

 

Add 5 to both sides:
x = 5 or x + 1 = 0

 

Subtract 1 from both sides:
x = 5                or                x = -1

Guest Nov 17, 2017
edited by Guest  Nov 17, 2017

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