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Solve `x^2-4x-4=0` 

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user4825270 | Student | eNoter

Posted July 29, 2013 at 7:35 PM via web

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Solve `x^2-4x-4=0` 

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lfryerda | High School Teacher | (Level 2) Educator

Posted July 29, 2013 at 8:12 PM (Answer #1)

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To solve this equation, we cannot factor it using integers or rational values, so instead we need to use the quadratic formula.

For the quadratic equation `ax^2+bx+c=0` , the quadratic formula is

`x={-b+-sqrt{b^2-4ac}}/{2a}`

In this case, a=1, b=-4 and c=-4, so the solutions to the equation are

`x={4+-sqrt{16-4(-4)}}/2`   simplify the square root

`={4+-sqrt32}/2`  simplify the radical

`={4+-sqrt16sqrt2}/2`  

`={4+-4sqrt2}/2`   cancel common factor of 2 in numerator and denominator

`=2+-2sqrt2`

The solutions of the equation are `x=2+2sqrt2` and `x=2-sqrt2` .

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