quadratic formulas: x squared minus 1= 2x

Question

^x2-1=2x

Answer 1

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

Answer 2

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!!!!!!!!!!!!!!!!!!!!!!!