^{x2}-1=2x

^{2}- 1 = 2x

^{2}+bx+c=0):

^{2}- 2x -1 = 0

^{2}- 4ac)

^{1/2}

^{2}- 4(1)(-1)]

^{1/2}

^{1/2}

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor

x^{2} - 1 = 2x

First, put the equation into standard form (ax^{2}+bx+c=0):

x^{2} - 2x -1 = 0

This equation does not factor readily, so let's use the Quadratic Formula:

x = (-b/2a) ± (1/2a)(b^{2} - 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

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

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

So (2-√8)/2 = 1 ± √2

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