Solve `x^2-4x-4=0` 

1 Answer

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lfryerda | High School Teacher | (Level 2) Educator

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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


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


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