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quadratic formulas: x squared minus 1= 2x

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2 Answers

x2 - 1 = 2x
 
First, put the equation into standard form (ax2+bx+c=0):
 
x2 - 2x -1 = 0
 
This equation does not factor readily, so let's use the Quadratic Formula:
 
x = (-b/2a) ± (1/2a)(b2 - 4ac)1/2
 
For your problem, a=1, b=-2, and c=-1:
 
x = (2/2) ± (1/2)[(-2)2 - 4(1)(-1)]1/2
 
x = 1 ± (1/2)[4 + 4]1/2
 
x = 1 ± (1/2)(√8) = 1 ± (1/2)(2√2)
 
x = 1+√2 and 1-√2

Comments

same answer, sorry I repeated the problem Philip.

x2 - 1 = 2x; reorganizing the equation we obtain: X^2 - 2x -1
Quadratic solution: (-b ± √(b^2- 4ac))/2a
Then, plugging into the formula we have:
(2 ± √(4+(4*1*1))/2
x1 = (2 + √8)/2 = 2.41421
x2 = (2 - √8)/2 = 0.41421
CHECK!!!!!!!!!!!!!!!!!!!!!!!
 
 
 
 

Comments

(2-√8)/2 is not simplified.  √8 = √4*2 = 2√2.
 
So (2-√8)/2 = 1 ± √2

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